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The multicolour size-Ramsey number of powers of paths

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


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: 16 May 2024 03:46

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