Check the least number of colors needed to color graph (chromatic number in 2-regular graph)

Question

My task is to check the least number of colors used in graph coloring which is simply chromatic number of graph. My undirected graph is 2-regular (each vertex is 2-degree). I found solution that

(maximum independent set number)/number of vertices = number of colors (chromatic number)

https://i.stack.imgur.com/V00wK.jpg - how it looks like

As you see, it can be 2-colored if result is 2 or 3-colored if the result is more than 2.

But I have no idea how I could find an maximum independent set in such graph.

A 2-regular graph consists of disconnected cycles. Each cycle can be 2-colored if the number of vertices in it is even and 3-colored otherwise. — n. m. could be an AI, Jun 26 '19 at 10:57

score 1 · Accepted Answer · answered Jun 26 '19 at 10:58

1

A 2-regular graph is nothing more than a union of disjoint cycles. If any of the cycles have odd length then the chromatic number is 3, otherwise it's 2. It's that simple. You don't need an algorithm for this.

answered Jun 26 '19 at 10:58

Mu-Tsun Tsai

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Check the least number of colors needed to color graph (chromatic number in 2-regular graph)

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