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The 97 pages that link to Graph theory, each with the reason it gives.

• Paul ErdősNarrower topic: Erdős helped establish graph theory as a central setting for extremal and probabilistic questions.

• Directed graphNarrower topic: Directed graphs are one of the central structures studied in graph theory.

• Bipartite graphNarrower topic: Bipartite graphs are a basic graph class defined by how their edges join vertices.

• Pigeonhole principleNarrower topic: Finite graph colorings and degree counts often force repeated structures through the principle.

• Incidence matrixNarrower topic: Incidence matrices encode the vertices and edges that graph theory studies.

• Shortest path problemNarrower topic: The problem is defined on this structure of vertices and edges.

• Social network analysisNarrower topic: Its vertices and edges provide the formal language for representing social entities and ties.

• Breadth-first searchNarrower topic: Breadth-first search is a general method for exploring graph structures.

• Depth-first searchNarrower topic: DFS operates on this broader mathematical structure.

• Dijkstra's algorithmNarrower topic: Dijkstra's algorithm operates on weighted graphs and their paths.

• Ramsey theoryNarrower topic: Graph Ramsey theory applies its guarantees to colored edges and vertex configurations.

• Directed acyclic graphNarrower topic: Directed acyclic graphs are a fundamental graph-theoretic structure.

• Network topologyNarrower topic: It provides formal tools for representing and analyzing network topologies.

• Vertex (geometry)Narrower topic: Graphs use vertices as abstract points, even when no geometric position is assigned.

• Connected componentNarrower topic: Connected components are a basic structural feature studied throughout graph theory.

• Edge coloringNarrower topic: Edge coloring is a graph-theoretic problem about assigning labels to edges.

• Graph isomorphismNarrower topic: Graph isomorphism is a central notion for comparing structures studied in graph theory.

• HypergraphNarrower topic: Hypergraphs extend graph theory by allowing edges to join more than two vertices.

• Random graphNarrower topic: Random graphs are probability-distributed instances of the structures studied here.

• Road networkNarrower topic: Its graph models represent intersections as vertices and roads as edges.

• Simple graphNarrower topic: Simple graphs are a foundational kind of object in this field.

• Perfect matchingNarrower topic: Perfect matching is a central property studied in graphs.

• Recreational mathematicsNarrower topic: Networks and routes turn puzzles into questions about vertices, edges, and paths.

• Weighted graphNarrower topic: Weighted graphs extend ordinary graph structures by attaching values to edges.

• Adjacency listNarrower topic: Adjacency lists are a data representation for graphs.

• Transportation networkNarrower topic: Its models represent transport locations as vertices and routes as edges.

• Dependency graphNarrower topic: Dependency graphs apply graph-theoretic ideas to relations among components.

• ElementNarrower topic: Vertices and edges are commonly modeled as elements of sets.

• Extremal combinatoricsNarrower topic: Many extremal questions ask how many edges a graph can contain under a forbidden-pattern constraint.

• Network scienceNarrower topic: Provides the formal language for representing network structures.

• Path graphNarrower topic: Path graphs are among the simplest structures studied in graph theory.

• Spanning treeNarrower topic: Spanning trees are defined as subgraphs of graphs.

• Vehicle routing problemNarrower topic: Locations and travel links form the graph on which routes are planned.

• Eulerian pathNarrower topic: Eulerian paths are defined within graphs and concern how their edges can be traversed.

• Menger's theoremNarrower topic: Menger's theorem is a statement about paths and separation in graphs.

• Odd cycleNarrower topic: Odd cycles are defined and studied as structures inside graphs.

• Undirected graphNarrower topic: Undirected graphs are one of graph theory’s two fundamental edge-orientation models.

• Hamiltonian cycleNarrower topic: Hamiltonian cycles are defined by how edges connect and revisit a graph’s vertices.

• Handshaking lemmaNarrower topic: The lemma is a basic counting tool used throughout the subject.

• Petersen graphNarrower topic: The Petersen graph became a standard small example across many branches of graph theory.

• Seven Bridges of KönigsbergNarrower topic: Euler’s bridge abstraction helped launch this field.

• Brooks' theoremNarrower topic: Brooks' theorem is a central result about graph structure and coloring.

• Chromatic polynomialNarrower topic: Chromatic polynomials turn a graph’s adjacency structure into a counting function.

• Fused ringNarrower topic: Molecular rings can be represented as cycles in a graph of atoms and bonds.

• Regular graphNarrower topic: Regular graphs are a basic class within the broader study of graphs.

• Graph isomorphism problemNarrower topic: Graph isomorphism compares the structure of two such objects.

• Planar separator theoremNarrower topic: The theorem is a structural statement about finite graphs.

• Prim's algorithmNarrower topic: Prim's algorithm is defined on weighted graphs and exploits their connectivity.

• Spectral graph theoryNarrower topic: Spectral methods are one algebraic approach within the broader study of graphs.

• Wagner's theoremNarrower topic: Wagner’s theorem is a structural result about finite graphs.