| Texto completo | |
| Autor(es): |
Botler, Fabio
;
Moreira, Luiz
;
de Souza, Joao Pedro
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | DISCRETE MATHEMATICS; v. 349, n. 2, p. 6-pg., 2025-10-16. |
| Resumo | |
Given graphs G and H, we say that G is H-good if the Ramsey number R(G, H) equals the trivial lower bound (|G| - 1)(chi(H)-1) +sigma(H), where chi(H) denotes the usual chromatic number of H, and sigma(H) denotes the minimum size of a color class in a chi(H)-coloring of H. Pokrovskiy and Sudakov (2017) [17] proved that P-n is H-good whenever n >= 4|H|. In this paper, given epsilon > 0, we show that if H satisfies a special unbalance condition, then P(n )is H-good whenever n >= (2 + epsilon)|H |. More specifically, we show that if m(1), ...,m(k) are such that epsilon <middle dot> m(i) >= 2m(i-1)(2) for 2 <= i <= k, and n >= (2 + epsilon)(m(1) + <middle dot><middle dot> <middle dot>+m(k)), then P-n is Km(1),...,m(k)-good. (AU) | |
| Processo FAPESP: | 23/03167-5 - Combinatória clássica, assintótica, quântica e geométrica |
| Beneficiário: | Yoshiharu Kohayakawa |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 24/14906-6 - Partições e Coberturas de grafos |
| Beneficiário: | Fábio Happ Botler |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |