Combinatorics Graph Theory

Extremal Graph Theory and Forbidden Subgraphs

Studies maximum edge density in graphs avoiding specific subgraph structures using Turán-type theorems and extremal combinatorics.

RESEARCH GAP FRONTIERS

Ramsey Theory and Coloring Phenomena

Investigates existence of monochromatic structures in colored complete graphs and hypergraphs using probabilistic and algebraic methods.

RESEARCH GAP FRONTIERS

Spectral Graph Theory and Eigenvalue Methods

Analyzes graph properties through adjacency matrix eigenvalues and spectral methods to understand structural and dynamic behaviors.

RESEARCH GAP FRONTIERS

Random Graph Models and Phase Transitions

Examines Erdős–Rényi random graphs and their critical phenomena using probabilistic analysis and threshold behavior.

RESEARCH GAP FRONTIERS

Topological Graph Theory and Surface Embeddings

Studies graphs embedded on surfaces, genus calculations, and topological invariants using combinatorial topology methods.

RESEARCH GAP FRONTIERS

Hypergraph Matching and Covering Problems

Develops algorithms and bounds for matching, covering, and packing problems in hypergraphs using LP relaxations.

RESEARCH GAP FRONTIERS

Polynomial Method in Combinatorics

Applies algebraic polynomial techniques to solve discrete problems including set system and incidence geometry questions.

RESEARCH GAP FRONTIERS

Additive Combinatorics and Sum-Product Theorems

Studies additive structure of subsets in finite fields and groups using Fourier analysis and algebraic methods.

RESEARCH GAP FRONTIERS

Graph Homomorphisms and Constraint Satisfaction

Analyzes complexity and structure of homomorphism counts, CSP dichotomy, and related hardness phenomena.

Probabilistic Method in Graph Construction

Uses randomness to prove existence of graphs with extreme properties and constructs explicit expander families.

Graph Minor Theory and Excluded Minors

Studies structural characterizations of graph classes through minor-monotone properties and Robertson-Seymour theorem applications.

Expander Graphs and Mixing Properties

Constructs and analyzes sparse graphs with rapid mixing times using spectral gaps, zig-zag products, and applications.

Chromatic Polynomials and Deletion-Contraction

Investigates chromatic polynomial properties, root locations, and relationships to knot invariants and Tutte polynomials.

Perfect Graphs and Strong Perfect Graph Theorem

Studies properties of perfect graphs where chromatic and clique numbers coincide using forbidden subgraph characterizations.

Graph Isomorphism and Canonical Forms

Develops algorithms for graph isomorphism testing and computing canonical representations with applications to symmetry detection.

Network Flow and Combinatorial Optimization

Designs efficient algorithms for maximum flow, minimum cut, and related optimization problems using algebraic techniques.

Planar Graphs and Four Color Problem

Studies planar graph properties, outerplanarity, and extensions of the four color theorem to higher surfaces.

Matroid Theory and Graphic Matroids

Explores abstract matroid structures, independence systems, and connections to graph theory through graphic representations.

Graph Decomposition and Edge Coloring

Studies decomposition into cycles, paths, and Hamiltonian structures using matching theory and extremal methods.

Vertex Transitive Graphs and Cayley Graphs

Analyzes symmetric graph structures defined on groups using algebraic methods and spectral properties.

Algorithmic Game Theory on Graphs

Studies strategic behavior on networks, equilibrium computation, and graph-based auction mechanisms.

Probabilistic Combinatorics and Concentration

Applies concentration inequalities and martingale methods to analyze random structures in graphs and hypergraphs.

Bipartite Graphs and Matching Theory

Develops algorithms for perfect matchings, maximum matchings, and Hall theorem generalizations using network flows.

Graph Limits and Graphon Theory

Studies scaling limits of dense graphs using graphon functions and applies to large network analysis.

Approximation Algorithms for Graph Problems

Designs and analyzes approximation algorithms for NP-hard graph problems with complexity-theoretic lower bounds.

Dominating Sets and Graph Domination

Studies minimum dominating sets, total domination, and efficient domination in various graph classes.

Graph Coloring Heuristics and Algorithms

Develops practical and theoretical algorithms for vertex coloring with approximation guarantees and parameter dependence.

Cliques, Clique Covers, and Independence Numbers

Investigates computational complexity and bounds for finding maximum cliques and independent sets in various graph classes.

Directed Graphs and Tournaments

Studies properties of tournaments, strongly connected components, feedback arc sets, and score sequences.

Network Centrality Measures and Algorithms

Analyzes betweenness, closeness, and eigenvector centrality measures with efficient computation strategies.

Pathwidth, Treewidth, and Decompositions

Studies structural graph parameters and their use in designing fixed-parameter tractable algorithms.

Circular Chromatic Number and Extensions

Investigates fractional and circular colorings with applications to scheduling and resource allocation problems.

Hamiltonian Cycles and Path Problems

Studies existence, counting, and approximation of Hamiltonian structures in various graph families.

Vertex and Edge Connectivity Algorithms

Develops efficient algorithms for computing graph connectivity, minimum cuts, and flow-based applications.

Combinatorial Designs and Block Designs

Constructs and analyzes balanced incomplete block designs with optimal parameters using algebraic methods.

Incidence Geometry and Line-Point Structures

Studies incidence matrices, projective planes, and finite geometries using algebraic combinatorics.

Turán Problems for Hypergraphs

Extends extremal theory to hypergraphs and investigates maximum edge densities avoiding specific substructures.

Sparse Graph Limits and Graphon Convergence

Develops limit theory for sparse graphs using kernel and graphon-like objects with measure-theoretic foundations.

Strongly Regular Graphs and Parameters

Characterizes strongly regular graphs using eigenvalues, feasibility conditions, and algebraic constructions.

Distance Regular Graphs and Eigenvalues

Studies highly symmetric graphs with distance-transitive properties using spectral methods and representation theory.

Independent Set and Clique Approximations

Analyzes hardness of approximation for independent sets and clique problems with inapproximability results.

Graph Packing and Covering Theorems

Develops bounds and algorithms for packing and covering edge-disjoint copies of graphs in larger graphs.

Probabilistic Proofs and Lovász Local Lemma

Applies local lemma and derandomization techniques to construct combinatorial structures with properties.

Enumerative Combinatorics and Generating Functions

Counts combinatorial objects using generating functions, recurrence relations, and bijective methods.

Algebraic Combinatorics and Symmetric Functions

Studies symmetric function algebras, Schur functions, and applications to graph coloring and representations.

Coding Theory and Graph Codes

Designs error-correcting codes using graph structures, Tanner graphs, and LDPC code constructions.

Community Detection in Networks

Develops algorithms and statistical methods for discovering modular structure and clusters in large graphs.

Temporal and Dynamic Graphs

Studies graphs evolving over time with emphasis on temporal paths, reachability, and dynamic properties.

Graph Machine Learning and Neural Networks

Applies neural network architectures to graph-structured data including graph convolutions and attention mechanisms.

Quantum Walks and Graph Spectral Methods

Studies quantum random walks on graphs and quantum computational complexity of graph problems.

Fractional Chromatic Number and Relaxations

Studies the fractional and vector chromatic numbers of graphs as relaxations of the classical chromatic number with applications to approximation algorithms.

Extremal Combinatorics in Sparse Hypergraphs

Investigates extremal problems for hypergraphs with bounded sparsity conditions including maximum degrees and matching properties.

Regularity Lemma and Graph Partitioning

Develops and applies the Szemerédi Regularity Lemma and its extensions to partition large graphs into regular bipartite components.

Combinatorial Nullstellensatz and Applications

Uses algebraic geometry techniques via the Combinatorial Nullstellensatz to solve discrete combinatorial problems.

List Coloring and Choice Numbers

Studies list colorings where each vertex has an associated list of available colors and determines choosability of graphs.

Graph Parity and Even-Odd Decompositions

Analyzes decomposition of graphs into even and odd subgraphs with applications to network design and flow problems.

Balanced Partitions and Equipartitions

Studies partitions of graph vertex and edge sets into balanced components with applications to divide-and-conquer algorithms.

Odd Cycles and Signed Graph Theory

Investigates properties of signed graphs focusing on odd cycles, balance conditions, and structural characterizations.

Graph Rigidity and Geometric Realization

Studies the rigidity of graph embeddings in Euclidean space and determines which graphs can be realized with distance constraints.

Hypergraph Transversals and Hitting Sets

Analyzes transversal hypergraphs and optimal hitting set problems with applications to covering and packing duality.

Nowhere Zero Flow and Circular Flows

Studies nowhere zero flows on graphs and circular flows on orientations with connections to graph coloring.

Partial Steiner Systems and Resolvable Designs

Constructs and analyzes resolvable combinatorial designs and partial Steiner systems with optimal balance properties.

Subgraph Densities and Flag Algebras

Uses flag algebra methods to determine extremal densities of specific subgraphs in large graphs and hypergraphs.

Turán Density and Critical Exponents

Determines the asymptotic density of maximum size subgraphs avoiding forbidden configurations.

Bipartite Rainbow Matching Problems

Studies rainbow matchings in edge-colored bipartite graphs with applications to combinatorial optimization.

Graph Distinguishing Numbers and Automorphisms

Determines the minimum colors needed to distinguish vertices under all automorphisms of highly symmetric graphs.

Oriented Graph Homology and Cohomology

Develops homological and cohomological invariants for directed and oriented graphs from algebraic topology.

Covering Codes and Graph Distance Properties

Designs covering codes using graph distance metrics and analyzes their optimal cardinality and efficiency.

Biregular Bipartite Graphs and Canonical Forms

Classifies and enumerates biregular bipartite graphs with special focus on algebraic and combinatorial properties.

Forbidden Induced Subgraph Problems

Characterizes graphs and hypergraphs avoiding specific induced subgraph patterns with structural theorems.

Graph Circumference and Longest Cycles

Studies the length of longest cycles in graphs and relationships to connectivity and structural parameters.

Hypergraph Berge Cycles and Paths

Investigates cycles and paths in hypergraphs using Berge definitions with Ramsey-type extensions.

Equitable Partitions and Graph Quotients

Analyzes equitable partitions of graph vertex sets and the spectral properties of resulting quotient graphs.

Turán-type Problems for Ordered Graphs

Studies extremal problems in ordered and oriented graphs with forbidden pattern constraints.

Chromatic Stability and Threshold Phenomena

Analyzes how chromatic number changes under small perturbations and identifies phase transitions in random graphs.

Hypergraph Independence Number and Fractional Covers

Studies independence numbers in hypergraphs and fractional vertex covers using linear programming duality.

Acyclic Graph Colorings and Oriented Colorings

Investigates acyclic colorings avoiding monochromatic cycles and proper colorings of orientations.

Graph Modulo Prime Field Homomorphisms

Studies homomorphisms of graphs into Cayley graphs over finite fields and algebraic structures.

Pseudo-Random Graphs and Discrepancy Theory

Develops measures of pseudo-randomness for graphs and analyzes discrepancy bounds for vertex partition problems.

Graph Structure Decomposition Algorithms

Designs efficient algorithms for decomposing graphs into structural components with bounded complexity.

Vertex Labeling and Numbering Problems

Studies graceful labelings, magic labelings, and other vertex and edge numbering schemes on graphs.

Clique Intersection Graphs and Comparability

Characterizes graphs as clique intersection graphs and studies comparability and co-comparability properties.

Fractional Matching and Hall Marriage Theorem

Extends Hall marriage theorem and matching theory to fractional settings with continuous generalizations.

Degeneracy and Coloring Algorithms

Analyzes graph degeneracy as a structural measure and develops coloring algorithms using degeneracy ordering.

Ramsey Multiplicity and Exact Counts

Determines exact numbers of monochromatic copies of fixed subgraphs in edge colorings.

Three Dimensional Combinatorial Topology

Studies simplicial complexes and combinatorial structures arising from three-dimensional geometric configurations.

Generalized Turán Problems and Stability

Extends classical Turán problems to multiple forbidden configurations and determines extremal graph stability.

Random Bipartite Graph Properties

Analyzes probabilistic properties of random bipartite graphs including connectivity and expansion thresholds.

Graph Bandwidth and Channel Assignment

Studies bandwidth minimization in linear vertex orderings with applications to channel assignment problems.

Fractional Graph Homomorphism Densities

Determines densities of graph homomorphisms in limits using fractional viewpoints and optimization.

Hypergraph Packing and Independent Systems

Studies packing problems in hypergraphs maximizing the number of disjoint substructures.

Algebraic Topology of Simplicial Complexes

Applies algebraic topology methods to analyze homology and cohomology of combinatorial simplicial complexes.

Triangle-Free Graphs and Stability Numbers

Investigates structure of triangle-free graphs with bounds on independence number and other parameters.

Graph Saturation Problems and Growth

Studies minimum size graphs avoiding forbidden subgraphs while maintaining certain connectivity properties.

Clique Density and Ramsey Density Functions

Analyzes densities of cliques and related structures in large graphs through limit objects.

Oriented Matroid Realizability Theory

Studies geometric realizability of oriented matroids with applications to oriented graph structures.

Hypergraph Regularity and Counting Lemmas

Develops hypergraph versions of regularity lemmas with applications to asymptotic counting problems.

Factor and Decomposition in Regular Graphs

Studies factorization of regular graphs into spanning subgraphs with specified degree constraints.

Multiplicative Graph Structures and Lattices

Analyzes graphs arising from multiplicative structures on finite rings and lattice-theoretic properties.

Graph Contractions and Critical Graphs

Studies critical graphs that lose properties under edge contractions with applications to colorability.

Fractional Graph Coloring and Relaxations

Studies fractional chromatic numbers and linear programming relaxations of graph coloring problems with applications to optimization.

List Coloring and Choosability Parameters

Investigates list chromatic numbers, list edge coloring, and choosability bounds for various graph classes.

Graph Saturation and Turán-type Problems

Examines saturation numbers and extremal densities for families of graphs avoiding specific configurations.

Oriented Graph Colorings and Homomorphisms

Studies chromatic properties and homomorphism densities in orientations of undirected graphs.

Bootstrap Percolation on Graphs

Analyzes threshold phenomena and cascade dynamics in graph-based bootstrap percolation processes.

Graph Burning and Firefighter Problems

Investigates spreading processes and defense strategies on graphs motivated by fire propagation models.

Localization and Metric Dimension

Studies resolving sets, metric dimension, and uniqueness of vertex identification in graphs.

Graph Bandwidth and Layout Problems

Examines linear arrangements, bandwidth minimization, and related graph layout optimization problems.

Probabilistic Existence of Graph Structures

Uses probabilistic methods to establish existence of graphs with specified chromatic, spectral, or structural properties.

Vertex Cover Kernelization and Parameterization

Develops fixed-parameter tractable algorithms and kernel bounds for vertex cover and related problems.

Hypergraph Coloring and Fractional Covers

Studies chromatic numbers of hypergraphs and fractional transversal numbers with applications to combinatorial problems.

Graceful Labeling and Graph Decompositions

Investigates graceful, harmonious, and sequential labelings with connections to graph decomposition conjectures.

Nowhere Zero Flows and Cycle Covers

Examines integer flows, flow polynomials, and cycle cover problems on graphs and directed graphs.

Reconstruction and Graph Invariants

Studies the graph reconstruction conjecture and development of discriminating invariants for graph identification.

Ramanujan Graphs and Spectral Gaps

Constructs and analyzes Ramanujan graphs with optimal spectral gap properties for network applications.

Synchronization and Graph Synchrony

Studies coupled oscillators and synchronization dynamics on graph topologies and network structures.

Distinguishing Number and Symmetry Breaking

Investigates colorings that break all non-trivial automorphisms and the distinguishing number of graphs.

Geometric Graph Theory and Euclidean Metrics

Studies unit distance graphs, geometric graph realizability, and distance-constrained graph properties.

Graph Limits and Dense Graph Limits

Develops theory of dense graph sequences, their limits via graphons, and convergence properties.

Sparse Degeneracy and Coloring Bounds

Analyzes degeneracy-based coloring bounds and chromatic number estimates for sparse graph classes.

Fractional Matching and Hall Conditions

Studies fractional matchings, covers, and generalizations of Hall''s theorem in graph theory.

Tradeoffs in Graph Partitioning

Investigates fundamental tradeoffs between partition quality, balance, and separator sizes in graph division.

Combinatorial Nullstellensatz and Applications

Applies algebraic nullstellensatz results to prove existence and bounds for graph-theoretic structures.

Distributed Graph Algorithms and Complexity

Analyzes local algorithms, communication complexity, and distributed computation on graph networks.

Intersecting Families and Fisher Inequality

Studies intersecting set systems, Sperner properties, and their applications to graph combinatorics.

Graph Packing with Size Constraints

Examines packing problems for graphs with restricted sizes, densities, and resource constraints.

Clustering Coefficients and Transitivity

Studies local clustering measures, transitivity properties, and their relationships in real networks.

Probabilistic Graph Existence Theorems

Establishes existence of graphs with prescribed property combinations using probabilistic and entropy methods.

Balanced Graph Partitioning and Separators

Studies balanced vertex separators, edge separators, and their applications to divide-and-conquer algorithms.

Subgraph Density and Regularity Lemmas

Applies Szemeredi''s regularity lemma and partition refinements to analyze subgraph densities and counts.

Graph Homomorphism Densities and Limits

Studies homomorphism densities between graphs, their limiting behavior, and extremal problems.

Antimagic and Labeling Conjectures

Investigates antimagic labelings, total labelings, and related open conjectures in graph labeling theory.

Threshold Graphs and Comparability Orders

Characterizes threshold graphs, comparability graphs, and their role in graph recognition algorithms.

Coloring Random Regular Graphs

Analyzes chromatic number behavior and coloring algorithms for random d-regular graph models.

Hypergraph Transversals and Hitting Sets

Studies minimum transversals, hitting set complexities, and approximation for hypergraph covering.

Graph Planarity Testing and Algorithms

Develops efficient planarity testing algorithms and characterizations of nonplanar graph structures.

Stochastic Graph Models and Inference

Studies statistical inference on random graphs, block models, and latent space graph representations.

Gallai Graphs and Perfect Orderings

Investigates perfect graphs, perfect orderings, and Gallai decompositions in graph theory.

Vertex Isoperimetric Problems

Studies sets minimizing vertex boundary relative to interior size in graphs and hypergraphs.

Temporal Network Dynamics and Evolution

Analyzes dynamic processes including spreading, diffusion, and adaptation on time-varying graphs.

Efficient Graph Sparsification Methods

Develops techniques to preserve graph properties while reducing edges through sparsification algorithms.

Equitable Graph Colorings and Partitions

Studies colorings where color class sizes differ by at most one with applications to load balancing.

Crossing Number and Graph Drawings

Investigates crossing numbers, rectilinear drawings, and graph visualization optimization problems.

Structural Graph Parameters and Bounds

Establishes relationships between structural parameters like arboricity, degeneracy, and coloring numbers.

Set Systems and Covering Designs

Studies optimal covering designs, covering arrays, and their applications to combinatorial testing.

Influence and Centrality in Networks

Analyzes network influence propagation, centrality measures, and their algorithmic computation.

Online Graph Coloring and Algorithms

Studies competitive ratios and approximation guarantees for online graph coloring problems.

Graph Minors and Kuratowski Subgraphs

Explores forbidden minors, Kuratowski graphs, and structural characterizations of minor-closed families.

Fractional and List Coloring Extensions

Study of fractional chromatic numbers and list coloring variants where vertices are assigned from predefined color lists with probabilistic constraints.

Algorithmic Aspects of Graph Automorphisms

Investigation of computational complexity and efficient algorithms for computing automorphism groups and orbits of graph vertices.

Clique-Width and NLC-Width Parameters

Analysis of graph complexity measures based on recursive decompositions with bounded clique-width and their algorithmic implications.

Extremal Problems for Oriented Graphs

Study of maximum and minimum sizes of directed graphs avoiding specific tournament and digraph structures.

Homomorphism Density and Graphon Calculus

Investigation of counting homomorphisms in dense graph sequences using graphon limits and variational methods.

Nowhere Zero Flows and Tutte Conjectures

Research on integer-valued flows on graphs avoiding zero and connections to Tutte''s cycle double cover conjecture.

Bandwidth and Graph Layouts Optimization

Study of linear arrangements minimizing maximum distances between adjacent vertices and generalizations to multi-dimensional layouts.

Subgraph Isomorphism and Pattern Matching

Computational and structural complexity of detecting and counting subgraph patterns in large-scale graphs.

Steiner Trees and Network Design

Approximation algorithms and exact methods for connecting vertex subsets with minimal total edge weight in networks.

Balanced Vertex Separators and Cuts

Study of minimum-size vertex sets whose removal creates balanced components with applications to divide-and-conquer algorithms.

Combinatorial Curvature in Graph Networks

Investigation of discrete curvature measures on graphs capturing local geometric properties and network topology.

Pseudo-Randomness and Graph Mixing Times

Analysis of expansion properties and convergence rates for random walks on graphs with applications to derandomization.

Incidence Colorings and Neighbor-Distinguishing

Study of edge-vertex colorings ensuring incident edges have distinct colors and generalized distinguishing colorings.

Graph Packing with Size and Density Constraints

Research on partitioning edges of large graphs into copies of specific subgraph structures with optimality guarantees.

Signed Graph Coloring and Switching Equivalence

Study of proper colorings in graphs with signed edges and classification under switching operations.

Sparse Random Matrix and Graph Spectra

Analysis of spectral properties of random sparse graph adjacency matrices and universality in extreme eigenvalues.

Combinatorial Optimization on Hypergraphs

Development of algorithmic techniques for optimization problems defined on hypergraph structures with applications.

Critical Structures and Deletion Sensitivity

Identification and characterization of minimally critical subgraphs for various graph properties under edge and vertex removal.

Graph Bottleneck Identification and Analysis

Methods for detecting articulation points, bridges, and structures whose removal significantly impacts connectivity.

Biased Games on Graphs and Strategies

Study of combinatorial games on graph structures with asymmetric resources and optimal strategy analysis.

Generalized Vertex Cover and Hitting Sets

Approximation algorithms and hardness results for variants of vertex cover with weighted and geometric constraints.

Metrical Dimension and Resolving Sets

Study of minimum vertex sets that uniquely identify all vertices by distance sequences with applications to network localization.

Spanning Subgraph Enumeration Techniques

Combinatorial and algorithmic methods for counting and generating spanning subgraphs satisfying structural properties.

Density-Sensitive Approximation Algorithms

Design of approximation algorithms with performance ratios depending on graph density and sparsity measures.

Vertex Ranking and Tree Decomposition Width

Study of optimal vertex orderings minimizing maximum rank depth with connections to treewidth and pathwidth.

Monochromatic Components in Colored Graphs

Analysis of connectivity and structure of color-class-induced subgraphs in edge and vertex colored graphs.

Algorithmic Lovász Local Lemma Applications

Derandomization and algorithmic applications of the Lovász Local Lemma to construct graphs with specified properties.

Forbidden Induced Subgraph Characterizations

Complete structural characterization of graph classes defined by sets of forbidden induced subgraphs.

Network Resilience and Fault Tolerance

Study of graph structures and algorithms ensuring network functionality under cascading failures and edge removals.

Combinatorial Sketching and Data Structures

Development of space-efficient graph data structures using sketching techniques for approximate computations.

Circular Patterns and Cyclic Orderings

Study of combinatorial structures arising from cyclic arrangements and rotational symmetries in graph theory.

Modularity and Community Structure Optimization

Algorithmic methods for maximizing modularity scores and identifying densely connected vertex communities.

Graph Sparsification and Effective Resistance

Construction of sparse subgraphs preserving electrical properties and spectral information from original graphs.

Oriented Coloring and Dichromatic Number

Study of proper colorings in oriented graphs where adjacent vertices and their orientation have distinct colors.

Combinatorial Perturbation and Stability

Analysis of how small structural changes affect graph properties and robustness of combinatorial conclusions.

Geometric Graph Realization Problems

Investigation of realizability of abstract graphs as geometric graphs in Euclidean spaces with distance constraints.

Hypergraph Transversals and Hitting Complexity

Study of minimum hitting sets for hypergraph structures and connections to covering and packing duality.

Synchronization and Orientation Recovery

Recovery of consistent orientations and labelings from noisy pairwise comparisons using spectral methods.

Directed Acyclic Graph Layouts and Scheduling

Optimal ordering and visualization techniques for DAGs with applications to job scheduling and data dependencies.

Parameterized Complexity of Graph Problems

Analysis of algorithmic tractability of NP-hard graph problems when parameterized by structural measures.

Hyperbolic Geometry and Graph Embeddings

Embedding graphs in hyperbolic spaces preserving distances and studying applications to hierarchical networks.

Assortativity and Degree Correlations

Analysis of patterns in degree-degree correlations affecting network robustness and clustering phenomena.

List Edge Coloring and Choosability

Study of edge colorability when colors available to each edge depend on incident vertices and edges.

Influence Maximization and Cascade Models

Approximation algorithms for selecting seed vertices maximizing influence spread under propagation models.

Implicit Representation and Space Bounds

Study of implicit graph representations using minimal space with query-efficient access to adjacencies.

Multigraph Embeddings and Multiplicity Effects

Analysis of structural and spectral properties of multigraphs with multiple edges between vertex pairs.

Lattice Coloring and Geometric Combinatorics

Chromatic properties of graphs induced by lattice points with geometric distance and divisibility constraints.

Nash Equilibria in Graph Formation Games

Strategic analysis of equilibrium graph structures when agents decide edge formation to maximize utility.

Expansion and Mixing of Weighted Graphs

Study of expansion properties and spectral gaps in weighted and valued graphs with applications to mixing.

Correlation Clustering and Structural Optimization

Approximation algorithms for clustering vertices minimizing disagreement with similarity and dissimilarity constraints.

Quasirandomness and Regularity Lemmas

Investigation of structural properties that make graphs behave like random graphs, including Szemeredi''s regularity lemma and its applications to counting and testing problems.

Distributed Algorithms on Network Graphs

Study of decentralized computation and decision-making on graphs where nodes have limited information and must coordinate locally to solve global optimization problems.