Coloring Number Of A Graph
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Conversely if a graph can be 2 colored it is bipartite since all edges connect vertices of different colors. Bipartite graphs with at least one edge have chromatic number 2 since the two parts are each independent sets and can be colored with a single color. A graph with clique number 3 and chromatic number 4.
Chromatic number is the minimum number of colors required to properly color any graph.
The smallest number of colors needed to color a graph g is called its chromatic number and is often denoted χ g. Sometimes γ g is used since χ g is also used to denote the euler characteristic of a graph. A graph that can be assigned a proper k coloring is k colorable and it is k chromatic if its chromatic number is exactly k. Vertex coloring is an assignment of colors to the vertices of a graph g such that no two adjacent vertices have the same color.
Simply put no two vertices of an edge should be of the same color. The minimum number of colors required for vertex coloring of graph g is called as the chromatic number of g denoted by x g. χ g 1 if and only if g is a null graph. If g is not a null graph then χ g 2.
This graph is not 2 colorable this graph is 3 colorable this graph is 4 colorable. The chromatic number of a graph is the minimal number of colors for which a graph coloring is possible. This definition is a bit nuanced though as it is generally not immediate what the minimal number is. Vertex coloring is an assignment of colors to the vertices of a graph g such that no two adjacent vertices have the same color.
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Simply put no two vertices of an edge should be of the same color. The minimum number of colors required for vertex coloring of graph g is called as the chromatic number of g denoted by x g. χ g 1 if and only if gx is a null graph. If gx is not a null graph then χ g 2.
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