Han, Jie, Kohayakawa, Yoshiharu, Letzter, Shoham, Mota, Guilherme Oliveira and Parczyk, Olaf (2021) The size-Ramsey Number of 3-uniform tight paths. Advances in Combinatorics, 2021 (1). ISSN 2517-5599
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Abstract
Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists a hypergraph G with m edges with the property that in any colouring of the edges of G with two colours there is a monochromatic copy of H. We prove that the size-Ramsey number of the 3-uniform tight path on n vertices Pn(3) is linear in n, i.e., ˆr2(Pn(3)) = O(n). This answers a question by Dudek, La Fleur, Mubayi, and Rödl for 3-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417–434], who proved ˆr2(Pn(3)) = O(n3/2 log3/2 n).
Item Type: | Article |
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Official URL: | https://www.advancesincombinatorics.com/ |
Additional Information: | © 2021 The Authors |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 07 Apr 2022 11:30 |
Last Modified: | 05 Oct 2024 05:33 |
URI: | http://eprints.lse.ac.uk/id/eprint/114616 |
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