Question: Is a petersen graph 2-colorable? Is it 3-colorable? A graph is 3-colorable if we can color every vertex with one of 3 colors (say, red,

Is a petersen graph 2-colorable? Is it 3-colorable? A graph is 3-colorable if we can color every vertex with one of 3 colors (say, red, blue, green) so that no edge is monochromatic, i.e., every edge must have endpoints of different colors. Show that if we delete any vertex from the Petersen graph, then the re- sulting graph will have a hamilton cycle. (hint: symmetry)

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