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5:2-coloring of Dodecahedral graph. A 4:2-coloring of this graph does not exist. Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring. In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those ...
Complete coloring; Edge coloring; Exact coloring; Four color theorem; Fractional coloring; Goldberg–Seymour conjecture; Graph coloring game; Graph two-coloring; Harmonious coloring; Incidence coloring; List coloring; List edge-coloring; Perfect graph; Ramsey's theorem; Sperner's lemma; Strong coloring; Subcoloring; Tait's conjecture; Total ...
An edge coloring of is called a -rainbow coloring if for every set of vertices of , there is a rainbow tree in containing the vertices of . The k {\displaystyle k} -rainbow index rx k ( G ) {\displaystyle {\text{rx}}_{k}(G)} of G {\displaystyle G} is the minimum number of colors needed in a k {\displaystyle k} -rainbow coloring of G ...
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The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.
An incidence coloring of a graph is an assignment of a color to each incidence of G in such a way that adjacent incidences get distinct colors. It is equivalent to a strong edge coloring of the graph obtained by subdivising each edge of G {\displaystyle G} once.
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