Minimum Number of k-Cliques in Graphs with Bounded Independence Number
Combinatorics
2015-03-20 v4
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).
Keywords
Cite
@article{arxiv.1203.4393,
title = {Minimum Number of k-Cliques in Graphs with Bounded Independence Number},
author = {Oleg Pikhurko and Emil R. Vaughan},
journal= {arXiv preprint arXiv:1203.4393},
year = {2015}
}
Comments
25 pages. v4: Three new solved cases added: (3,5), (3,6), (3,7). All calculations are done with Version 2.0 of Flagmatic now