chromatic number of regular graph

Question

What is the vertex chromatic number of regular graph?

Regular graph is a graph where each vertex has the same number of neighbors; i.e.

every vertex has the same degree or valency.

Can you help me?

Answer 1

There's a range of possibilities. Say we're looking at $100$-regular graphs. One possibility is the complete graph $K_{101}$, which has a chromatic number of $101$. Another possibility is the complete bipartite graph $K_{100,100}$, which has a chromatic number of $2$. Anything in between is also possible.