| Full text | |
| Author(s): |
Aragao, Lucas
;
Marciano, Joao Pedro
;
Mendonca, Walner
Total Authors: 3
|
| Document type: | Journal article |
| Source: | EUROPEAN JOURNAL OF COMBINATORICS; v. 124, p. 12-pg., 2024-10-18. |
| Abstract | |
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) | |
| FAPESP's process: | 23/07695-6 - Monochromatic tilings and covers problems |
| Grantee: | Walner Mendonça dos Santos |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |