Maximum number of edge colorings avoiding rainbow copies of $K_4$
Combinatorics
2025-05-02 v2
Abstract
In this paper we show that for and any sufficiently large -vertex graph the number of -edge-colorings of with no rainbow is at most , where denotes the Tur\'{a}n number of . Moreover, attains equality if and only if it is the Tur\'{a}n graph . The bound on the number of colors is best possible. It improves upon a result of H. Lefmann, D.A. Nolibos, and the second author who showed the same result for and it confirms a conjecture by Gupta, Pehova, Powierski and Staden.
Cite
@article{arxiv.2503.19244,
title = {Maximum number of edge colorings avoiding rainbow copies of $K_4$},
author = {Hiêp Hàn and Carlos Hoppen and Nicolas Moro Müller and Dionatan Ricardo Schmidt},
journal= {arXiv preprint arXiv:2503.19244},
year = {2025}
}
Comments
15 pages