Regular Tur\'an numbers and some Gan-Loh-Sudakov-type problems
Combinatorics
2020-09-14 v2
Abstract
Motivated by a Gan-Loh-Sudakov-type problem, we introduce the regular Tur\'an numbers, a natural variation on the classical Tur\'an numbers for which the host graph is required to be regular. Among other results, we prove a striking supersaturation version of Mantel's theorem in the case of a regular host graph of odd order. We also characterise the graphs for which the regular Tur\'an numbers behave classically or otherwise.
Keywords
Cite
@article{arxiv.1911.08452,
title = {Regular Tur\'an numbers and some Gan-Loh-Sudakov-type problems},
author = {Stijn Cambie and Rémi de Joannis de Verclos and Ross J. Kang},
journal= {arXiv preprint arXiv:1911.08452},
year = {2020}
}
Comments
16 pages, 2 figures, 1 table