The Threshold for the Balancedness of Colored Graphs
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چکیده
Let Col n denote the set of all `-colored graphs on n vertices and let G be a graph drawn uniformly at random from this set. Provided that `→∞, we prove that all color classes of G deviate roughly at most √ 2 log ` from ⌊ n ` ⌋ , and there is at least one color class with such deviation. Furthermore, we prove similar results for the class Col n,M , which contains all `-colored graphs with precisely M = cn edges, for 0 < c < 12 .
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تاریخ انتشار 2006