Han, J;
Kohayakawa, Y;
Letzter, S;
Mota, GO;
Parczyk, O;
(2021)
The Size-Ramsey Number of 3-uniform Tight Paths.
Advances in Combinatorics
, 2021
(1)
10.19086/aic.24581.
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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).
| Type: | Article |
|---|---|
| Title: | The Size-Ramsey Number of 3-uniform Tight Paths |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.19086/aic.24581 |
| UCL classification: | UCL 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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