More non-bipartite forcing pairs
Abstract
We study pairs of graphs (H_1,H_2) such that every graph with the densities of H_1 and H_2 close to the densities of H_1 and H_2 in a random graph is quasirandom; such pairs (H_1,H_2) are called forcing. Non-bipartite forcing pairs were first discovered by Conlon, Han, Person and Schacht [Weak quasi-randomness for uniform hypergraphs, Random Structures Algorithms 40 (2012), 1-38]: they showed that (K_t,F) is forcing where F is the graph that arises from K_t by iteratively doubling its vertices and edges in a prescribed way t times. Reiher and Schacht [Forcing quasirandomness with triangles, Forum of Mathematics, Sigma 7, 2019] strengthened this result for t=3 by proving that two doublings suffice and asked for the minimum number of doublings needed for t>3. We show that (t+2)/2 doublings always suffice.
Keywords
Cite
@article{arxiv.1906.04089,
title = {More non-bipartite forcing pairs},
author = {Tamas Hubai and Dan Kral and Olaf Parczyk and Yury Person},
journal= {arXiv preprint arXiv:1906.04089},
year = {2019}
}