English

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

R2 v1 2026-06-23T12:21:04.578Z