| Texto completo | |
| Autor(es): |
Aragao, Lucas
;
Marciano, Joao Pedro
;
Mendonca, Walner
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | EUROPEAN JOURNAL OF COMBINATORICS; v. 124, p. 12-pg., 2024-10-18. |
| Resumo | |
A classical result of Chv & aacute;tal implies that if n > (r - 1)(t - 1) + 1, then any colouring of the edges of K-n in red and blue contains either a monochromatic red K-r or a monochromatic blue Pt. We study a natural generalisation of his result, determining the exact minimum degree condition for a graph G on n = (r -1)(t -1)+1 vertices which guarantees that the same Ramsey property holds in G. In particular, using a slight generalisation of a result of Haxell, we show that delta(G) > n - (sic)t/2(sic) suffices, and that this bound is best possible. We also use a classical result of Bollob & aacute;s, Erdos, and Straus to prove a tight minimum degree condition in the case r = 3 for all n > 2t - 1. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text (AU) | |
| Processo FAPESP: | 23/07695-6 - Problemas de particionamentos e coberturas monocromáticas |
| Beneficiário: | Walner Mendonça dos Santos |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |