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arXiv · 1203.4393

Minimum Number of k-Cliques in Graphs with Bounded Independence Number

Oleg Pikhurko·Emil R. Vaughan
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Abstract

Erdos asked in 1962 about the value of f(n,k,l), the minimum number of k-cliques in a graph of order n and independence number less than l. The case (k,l)=(3,3) was solved by Lorden. Here we solve the problem (for all large n) when (k,l) is (3,4), (3,5), (3,6), (3,7), (4,3), (5,3), (6,3), and (7,3). Independently, Das, Huang, Ma, Naves, and Sudakov did the cases (k,l)=(3,4) and (4,3).

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Oleg Pikhurko, Emil R. Vaughan. 2013-04-27. Minimum Number of k-Cliques in Graphs with Bounded Independence Number. https://arxiv.org/abs/1203.4393

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