Han, J;
Kohayakawa, Y;
Letzter, S;
Mota, GO;
Parczyk, O;
(2021)
The size-Ramsey number of 3-uniform tight paths.
(In press).
![[img]](https://discovery.ucl.ac.uk/style/images/fileicons/text.png) |
Text
1907.08086v2.pdf - Accepted version Access restricted to UCL open access staff until 21 May 2021. Download (219kB) |
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 |
Archive Staff Only
 |
View Item |
