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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 ...
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A list edge-coloring is a choice of a color for each edge, from its list of allowed colors; a coloring is proper if no two adjacent edges receive the same color. A graph G is k -edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has a proper ...
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.
If colored, the number clues are also colored to indicate the color of the squares. Two differently colored numbers may or may not have a space in between them. For example, a black four followed by a red two could mean four black boxes, some empty spaces, and two red boxes, or it could simply mean four black boxes followed immediately by two ...
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. [12]
The smallest possible number of vertices of G is the induced Ramsey number r ind (H). Sometimes, we also consider the asymmetric version of the problem. We define r ind ( X , Y ) to be the smallest possible number of vertices of a graph G such that every coloring of the edges of G using only red or blue contains a red induced subgraph of X or ...
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 ...