Let G=(p,q) be a regular connected graph with q>p-1 and regularity r and girth g. Ç
Let H(p,q) be a graph which is chromatically equivalent to G.
Is it true that H must be r-regular and with girth g ?
I believe that it is true, but I have not able to prove it.
I dont think this is true.
Do you hace a counter example ?
will let you know shortly
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