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A graph is called an $(r,k)$-graph if its vertex set can be partitioned into $r$ parts of size at most $k$ with at least one edge between any two parts. Let $f(r,H)$ be the minimum $k$ for which there exists an $H$-free $(r,k)$-graph. In this paper w
Externí odkaz:
http://arxiv.org/abs/2308.16728
Autor:
Byrne, John, Tait, Michael
We study the function $H_n(C_{2k})$, the maximum number of Hamilton paths such that the union of any pair of them contains $C_{2k}$ as a subgraph. We give upper bounds on this quantity for $k\ge 3$, improving results of Harcos and Solt\'esz, and we s
Externí odkaz:
http://arxiv.org/abs/2304.02164
Autor:
Freitas, Bárbara Luíza Souza, Fava, Natália Melo de Nasser, Melo-Neto, Murilo Guilherme de, Dalkiranis, Gustavo Gonçalves, Tonetti, Adriano Luiz, Byrne, John Anthony, Fernandez-Ibañez, Pilar, Sabogal-Paz, Lyda Patricia
Publikováno v:
In Water Research 15 November 2024 266
