Coloring sparse random Cayley graphs
Abstract
It is shown that there exists c > 0 so that the Cayley graph over any finite abelian group Z generated by c |Z| random elements is properly 3-colorable with high probability (as |Z| ∞). This is asymptotically tight and improves the best-known bound due to Alon of 14 |Z| elements. It also makes progress toward Alon's suggestion that a bound of c |G| may hold for any finite solvable group G.
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