Category

Graph coloring

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four color theorem

statement in mathematics

assignment of colors to elements of a graph subject to certain constraints

an assignment of colors to the edges of a graph so that no two edges that share an endpoint have the same color as each other

five color theorem

chromatic polynomial

polynomial defined from a node-link graph, that counts the number of graph colorings as a function of the number of colors

Hadwiger–Nelson problem

mathematical problem

connected, bridgeless cubic graph with chromatic index equal to 4

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

Road coloring problem

theorem that every aperiodic strongly-connected out-regular directed graph can be labeled to give a synchronizable deterministic finite automaton

greedy coloring

coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color

undirected graph

tricolorability

thumb|right|A tricolored trefoil knot.In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial.

Hadwiger conjecture

conjecture that all graphs requiring k or more colors contain a k-vertex complete minor

generalization of graph coloring in which each vertex has a list of allowed colors

De Bruijn–Erdős theorem

theorem on coloring infinite graphs

complete coloring

graph coloring in which each color pair is represented by an edge of the graph

proper graph coloring of both vertices and edges

Grötzsch's theorem

theorem that every triangle-free planar graph is 3-colorable

Ringel–Youngs theorem

theorem on the number of colors needed for graphs embedded on higher genus surfaces

Erdős–Faber–Lovász conjecture

conjecture about coloring graphs formed by combining complete graphs

harmonious coloring

proper vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices

fractional coloring

topic in mathematical graph theory

graph invariant

Dinitz conjecture

theorem in combinatorics on the extension of arrays to partial Latin squares