| Full text | |
| Author(s): |
Han, Jie
;
Jenssen, Matthew
;
Kohayakawa, Yoshiharu
;
Mota, Guilherme Oliveira
;
Roberts, Barnaby
Total Authors: 5
|
| Document type: | Journal article |
| Source: | JOURNAL OF COMBINATORIAL THEORY SERIES B; v. 145, p. 17-pg., 2020-11-01. |
| Abstract | |
Given a positive integer s, a graph G is s-Ramsey for a graph H, denoted G -> (H)(s), if every s-colouring of the edges of G contains a monochromatic copy of H. The s-colour size-Ramsey number (r) over cap (s) (H) of a graph H is defined to be (r) over cap (s) (H) = min{vertical bar E(G)vertical bar: G -> (H)(s)}. We prove that, for all positive integers k and s, we have (r) over cap (s) (P-n(k)) = O(n), where P-n(k) is the kth power of the n-vertex path P-n. (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics |
| Grantee: | Guilherme Oliveira Mota |
| Support Opportunities: | Research Grants - Young Investigators Grants |