Graph Theory Bookmarks (Comprehensive)

Graph Theory (General) Graph theory Glossary of graph theory Outline of graph theory List of graph theory topics History of graph theory Seven Bridges of Königsberg
I. Fundamental Concepts Core Components Vertex / Node Edge / Link Loop (self-loop) Multiple edges Types of Graphs Directed graph (Digraph) Undirected graph Simple graph Multigraph Mixed graph Weighted graph Subgraph Induced subgraph Complement graph Line graph Infinite graph Graph Representations Adjacency list Adjacency matrix Incidence matrix Degree matrix Laplacian matrix LCF notation
II. Graph Properties & Invariants Connectivity & Distance Connectivity k-vertex-connected graph k-edge-connected graph Menger's theorem Path Walk Trail Cycle Distance Diameter Radius Girth Acyclic graph Directed acyclic graph (DAG) Coloring Graph coloring Vertex coloring Edge coloring Chromatic number Chromatic index Chromatic polynomial Total coloring List coloring Symmetry & Structure Graph automorphism Symmetric graph Vertex-transitive graph Edge-transitive graph Distance-transitive graph Strongly regular graph Distance-regular graph Density & Sparsity Dense graph Sparse graph Turán's theorem Embeddings & Drawings Graph drawing Planar graph Kuratowski's theorem Graph embedding Genus Toroidal graph Book thickness Queue number
III. Algorithms & Problems Traversal & Search Graph traversal Breadth-first search (BFS) Depth-first search (DFS) Shortest Path Shortest path problem Dijkstra's algorithm Bellman–Ford algorithm A* search algorithm Floyd–Warshall algorithm Spanning Trees Spanning tree Minimum spanning tree Prim's algorithm Kruskal's algorithm Borůvka's algorithm Flows & Cuts Flow network Maximum flow problem Max-flow min-cut theorem Ford–Fulkerson algorithm Edmonds–Karp algorithm Matching Matching Maximum cardinality matching Hopcroft–Karp algorithm Blossom algorithm Hall's marriage theorem Famous Problems & Theorems Eulerian path Hamiltonian path problem Travelling salesman problem Graph isomorphism problem Subgraph isomorphism problem Clique problem Independent set problem Vertex cover problem Four-color theorem Five-color theorem Brooks's theorem Vizing's theorem Ramsey's theorem Hadwiger–Nelson problem De Bruijn–Erdős theorem
IV. Special Classes of Graphs The Galleries of Named Graphs List of named graphs Basic Families Complete graph (Clique) Bipartite graph Complete bipartite graph Path graph Cycle graph Wheel graph Star graph Tree Forest Grid graph Regular & Symmetric Graphs Regular graph Cubic graph (3-regular) Cage Cayley graph Platonic solid graphs Archimedean graph Famous Named Graphs Petersen graph Generalized Petersen graph Heawood graph Pappus graph Desargues graph Dürer graph Möbius ladder Prism graph Shrikhande graph Clebsch graph Chvátal graph Frucht graph Tutte graph Gray graph Dyck graph Biggs–Smith graph Ljubljana graph Levi graph Snark Blanuša snarks Structural Properties Perfect graph Chordal graph Interval graph Unit distance graph Laman graph Well-covered graph Triangle-free graph Hamiltonian graph Hypohamiltonian graph
V. Advanced Topics & Subfields Spectral graph theory Extremal graph theory Topological graph theory Geometric graph theory Algorithmic graph theory Ramsey theory Random graph theory Network theory Chemical graph theory
VI. Related Mathematical Fields Combinatorics Set theory Linear algebra Eigenvalues and eigenvectors Topology Matroid theory Order theory Dilworth's theorem Structural rigidity
VII. Influential Mathematicians Leonhard Euler Paul Erdős W. T. Tutte Frank P. Ramsey Kazimierz Kuratowski Dénes Kőnig Claude Berge Pál Turán Arthur Cayley William Rowan Hamilton Nicolaas Govert de Bruijn Hugo Hadwiger György Hajós Leo Moser Edward Nelson Pappus of Alexandria Gérard Desargues Albrecht Dürer Danilo Blanuša Marion C. Gray Walther von Dyck