Question

Find the chromatic number of K5,4.​

Answer 1

Answer:

In a complete graph, with n vertices, you always need to use n colors. Suppose, that Kn can be colored with n−1 colors. Then there are 2 vertices with the same color, which, from definition are neighbours, and this results in contradiction. →χ(Kn)≥n.

In a graph with n vertices, χ will always be at maximum the number of vertices. χ(Kn)≤n.

→χ(Kn)=n.

Answer 2

Answer:

In a complete graph, with n vertices, you always need to use n colors. Suppose, that Kn can be colored with n−1 colors. Then there are 2 vertices with the same color, which, from definition are neighbours, and this results in contradiction. →χ(Kn)≥n.

In a graph with n vertices, χ will always be at maximum the number of vertices. χ(Kn)≤n.

→χ(Kn)=n.