The size-Ramsey number of powers of bounded degree trees

Berger, Sören, Kohayakawa, Yoshiharu, Maesaka, Giulia Satiko, Martins, Taísa, Mendonça, Walner, Mota, Guilherme Oliveira and Parczyk, Olaf (2021) The size-Ramsey number of powers of bounded degree trees. Journal of the London Mathematical Society, 103 (4). 1314 - 1332. ISSN 0024-6107

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Abstract

Given a positive integer (Formula presented.), the (Formula presented.) -colour size-Ramsey number of a graph (Formula presented.) is the smallest integer (Formula presented.) such that there exists a graph (Formula presented.) with (Formula presented.) edges with the property that, in any colouring of (Formula presented.) with (Formula presented.) colours, there is a monochromatic copy of (Formula presented.). We prove that, for any positive integers (Formula presented.) and (Formula presented.), the (Formula presented.) -colour size-Ramsey number of the (Formula presented.) th power of any (Formula presented.) -vertex bounded degree tree is linear in (Formula presented.). As a corollary, we obtain that the (Formula presented.) -colour size-Ramsey number of (Formula presented.) -vertex graphs with bounded treewidth and bounded degree is linear in (Formula presented.), which answers a question raised by Kamčev, Liebenau, Wood and Yepremyan.

Item Type:	Article
Official URL:	https://londmathsoc.onlinelibrary.wiley.com/journa...
Additional Information:	© 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	10 Jan 2022 10:51
Last Modified:	17 Apr 2024 18:15
URI:	http://eprints.lse.ac.uk/id/eprint/113369

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