Han, Jie, Jenssen, Matthew, Kohayakawa, Yoshiharu, Mota, Guilherme Oliveira and Roberts, Barnaby (2020) The multicolour size-Ramsey number of powers of paths. Journal of Combinatorial Theory. Series B, 145. 359 - 375. ISSN 0095-8956
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Identification Number: 10.1016/j.jctb.2020.06.004
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 rˆs(H) of a graph H is defined to be rˆs(H)=min{|E(G)|:G→(H)s}. We prove that, for all positive integers k and s, we have rˆs(Pnk)=O(n), where Pnk is the kth power of the n-vertex path Pn.
| Item Type: | Article |
|---|---|
| Additional Information: | © 2020 Elsevier Inc. |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 10 Jun 2022 08:09 |
| Last Modified: | 02 Nov 2024 18:06 |
| URI: | http://eprints.lse.ac.uk/id/eprint/115334 |
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