Non-bipartite k-common graphs
Combinatorics
2024-08-27 v7
Abstract
A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.
Cite
@article{arxiv.2006.09422,
title = {Non-bipartite k-common graphs},
author = {Daniel Kral and Jonathan A. Noel and Sergey Norin and Jan Volec and Fan Wei},
journal= {arXiv preprint arXiv:2006.09422},
year = {2024}
}
Comments
Fix of an incorrectly argued step in the proof of Lemma 12