Chromatic Number In Graph Coloring
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.
Chromatic number in graph coloring. Chromatic number the chromatic number of a graph is the smallest number of colors needed to color the vertices of so that no two adjacent vertices share the same color skiena 1990 p. Graph coloring chromatic number with solved examples graph theory classes in hindi graph theory video lectures in hindi for b tech m tech mca students. However a following greedy algorithm is known for finding the chromatic number of any given graph. A graph whose maximum clique is equal to its chromatic number is called perfect it was a famous open problem to classify all perfect graphs which was recently solved.
We introduced graph coloring and applications in previous post. Graph coloring algorithm there exists no efficient algorithm for coloring a graph with minimum number of colors. Easy engineering classes 77 845 views 11 42 vertex coloring and chromatic number. As discussed in the previous post graph coloring is widely used.
Example 5 8 2 if the vertices of a graph represent academic classes and two vertices are adjacent if the corresponding classes have people in common then a coloring of the vertices can be. Unfortunately there is no efficient algorithm available for coloring a graph with minimum number of colors as the problem is a known np complete problem. 210 i e the smallest value of possible to obtain a k coloring minimal. A graph coloring is an assignment of labels called colors to the vertices of a graph such that no two adjacent vertices share the same color.
A graph is perfect if and only if it is a berge graph. Graph coloring in graph theory graph coloring is a process of assigning colors to the vertices such that no two adjacent vertices get the same color. It is impossible to color the graph with 2 colors so the graph has chromatic number 3. A subset of vertices assigned to the same color is called a color class every such class forms an independent set.
Such that no two adjacent vertices share the same color. Graph coloring is a np complete problem. Graph coloring has many applications in addition to its intrinsic interest.
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