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The size-Ramsey Number of 3-uniform tight paths

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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Identification Number: 10.19086/aic.24581


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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Additional Information: © 2021 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 07 Apr 2022 11:30
Last Modified: 23 Jun 2024 23:22

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