How unproportional must a graph be?
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چکیده
Let uk(G, p) be the maximum over all k-vertex graphs F of by how much the number of induced copies of F in G differs from its expectation in the Erdős-Rényi random graph with edge probability p. This may be viewed as a measure of how close G is to being p-quasirandom. Our main result is that, for fixed k ≥ 4 and 0 < p < 1, the minimum of uk(G, p) over n-vertex graphs has order of magnitude Θ(n k−2).
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تاریخ انتشار 2014