An Optimal Coloring from a Body of Revolution
نویسندگان
چکیده
Consider the number of monochromatic k-cliques in an edge-two-coloring of the complete graph of order n. We determine asymptotically the best constant ck such that the number of one of the monochromatic k-cliques is less than ckn. For example, if k = 3 then c3 = μ3/6, where μ ≈ 0.65 is a root of z3−3z2 +1 = 0, and to get this c3 we translate the problem into a problem concerning the volume of a body of revolution. This translation is done by using the Gale–Ryser theorem on degree sequence of a bipartite graph.
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