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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.
Col is a pencil and paper game, specifically a map-coloring game, involving the shading of areas in a line drawing according to the rules of graph coloring. With each move, the graph must remain proper (no two areas of the same colour may touch), and a player who cannot make a legal move loses. The game was described and analysed by John Conway ...
Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring ...
Pages in category "Graph coloring" The following 82 pages are in this category, out of 82 total. ... Graph coloring game; Greedy coloring; Grötzsch's theorem;
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 coloring; Uniquely colorable graph
Incidence coloring game was first introduced by S. D. Andres. [15] It is the incidence version of the vertex coloring game, in which the incidences of a graph are colored instead of vertices. Incidence game chromatic number is the new parameter defined as a game-theoretic analogous of the incidence chromatic number.
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Graph coloring [2] [3]: GT4 Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph.