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The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f(v) to each vertex v, a graph G is f-choosable (or f-list-colorable) if it has a list coloring no matter how one assigns a list of f(v) colors to ...
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.
A proper distinguishing coloring is a distinguishing coloring that is also a proper coloring: each two adjacent vertices have different colors. The minimum number of colors in a proper distinguishing coloring of a graph is called the distinguishing chromatic number of the graph.
A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color.
Acyclic edge coloring is the edge-coloring variant of acyclic coloring, an edge coloring for which every two color classes form an acyclic subgraph (that is, a forest). [24] The acyclic chromatic index of a graph G {\displaystyle G} , denoted by a ′ ( G ) {\displaystyle a'(G)} , is the smallest number of colors needed to have a proper acyclic ...
In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.