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The size-Ramsey number of 3-uniform tight paths

Han, J; Kohayakawa, Y; Letzter, S; Mota, GO; Parczyk, O; (2021) The size-Ramsey number of 3-uniform tight paths. (In press).

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Abstract

Given a hypergraph H, the size-Ramsey number r^2(H) is the smallest integer m such that there exists a graph 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 P(3)n is linear in n, i.e., r^2(P(3)n)=O(n). This answers a question by Dudek, Fleur, Mubayi, and Rödl for 3-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417-434], who proved r^2(P(3)n)=O(n3/2log3/2n).

Type: Article
Title: The size-Ramsey number of 3-uniform tight paths
Publisher version: https://arxiv.org/abs/1907.08086#:~:text=We%20prov...
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10107285
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