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Minimum Number of k-Cliques in Graphs with Bounded Independence Number
OLEG PIKHURKO, EMIL R. VAUGHAN
Journal:

Combinatorics, Probability and Computing / Volume 22 / Issue 6 / November 2013

Published online by Cambridge University Press:

01 October 2013, pp. 910-934
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Erdős asked in 1962 about the value of f(n,k,l), the minimum number of k-cliques in a graph with 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) for (3,l) with 4 ≤ l ≤ 7 and (k,3) with 4 ≤ k ≤ 7. Independently, Das, Huang, Ma, Naves and Sudakov resolved the cases (k,l)=(3,4) and (4,3).

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