Category
page 1Theorems in graph theory
four color theorem
statement in mathematics
Ramsey's theorem
combinatorics theorem that any edge labeling of a sufficiently large complete graph contains monochromatic cliques
Max-flow min-cut theorem
theorem in optimization theory
Hall's marriage theorem
theorem that a finite bipartite graph has a perfect matching iff any subset of vertices from one group has a neighbourhood of equal or greater size
five color theorem
theorem
Kuratowski's theorem
a finite graph is planar iff it does not contain a subgraph that is a subdivision of K₅ or K₃,₃
Kirchhoff's theorem
theorem of computing the number of spanning trees in a graph
König's theorem
theorem showing that maximum matching and minimum vertex cover are equivalent for bipartite graphs
Menger's theorem
theorem characterizing graph connectivity by disjoint paths
Ore's theorem
theorem that a graph in which every two nonadjacent vertices have high degree sum must have a Hamiltonian cycle
Turán's theorem
theorem bounding the number of edges in a graph that has no large cliques
Brooks' theorem
theorem that, with two classes of exceptions, vertex-coloring a graph needs a number of colors at most equal to its maximum degree
Vizing's theorem
theorem in graph coloring
Robertson–Seymour theorem
mathematical theorem
Fáry's theorem
theorem that a planar graph admits straight drawings
Road coloring problem
theorem that every aperiodic strongly-connected out-regular directed graph can be labeled to give a synchronizable deterministic finite automaton
Tutte theorem
theorem giving a necessary and sufficient condition for a perfect matching to exist on a graph; generalization of Hall's marriage theorem
Berge's lemma
theorem in graph theory
Balinski's theorem
mathematical theorem concerning the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes
Robbins' theorem
theorem in graph theory
De Bruijn–Erdős theorem
theorem on coloring infinite graphs
Grötzsch's theorem
theorem that every triangle-free planar graph is 3-colorable
Wagner's theorem
characterization theorem in graph theory of planar graphs
Ringel–Youngs theorem
theorem on the number of colors needed for graphs embedded on higher genus surfaces
graph structure theorem
mathematical theorem
Schnyder's theorem
order dimension of incidences in planar graphs
Erdős–Burr conjecture
Frucht's theorem
theorem
BEST theorem
formula used in graph theory
Steinitz's theorem
Characterizes graphs formed by edges and vertices of 3-dimensional convex polyhedra
strong perfect graph theorem
perfect graphs have neither odd holes nor odd antiholes
perfect graph theorem
theorem in graph theory
Fleischner's theorem
theorem on Hamiltonian graphs
Grinberg's theorem
on Hamiltonian cycles in planar graphs
Erdős–Stone theorem
theorem in extremal graph theory
Petersen's theorem
every cubic bridgeless graph has a perfect matching