Upper Tails for Subgraph Counts in Random Graphs
نویسنده
چکیده
Let G be a fixed graph and let XG be the number of copies of G contained in the random graph G(n, p). We prove exponential bounds on the upper tail of XG which are best possible up to a logarithmic factor in the exponent. Our argument relies on an extension of Alon’s result about the maximum number of copies of G in a graph with a given number of edges. Similar bounds are proved for the random graph G(n, M) too.
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