Bucic, M;
Letzter, S;
Sudakov, B;
(2019)
Multicolour Bipartite Ramsey Number of Paths.
The Electronic Journal of Combinatorics
, 26
(3)
, Article P3.60. 10.37236/8458.
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Abstract
The k$-colour bipartite Ramsey number of a bipartite graph H is the least integer N for which every k -edge-coloured complete bipartite graph K N , N contains a monochromatic copy of H . The study of bipartite Ramsey numbers was initiated over 40 years ago by Faudree and Schelp and, independently, by Gyárfás and Lehel, who determined the 2 -colour bipartite Ramsey number of paths. Recently the 3 -colour Ramsey number of paths and (even) cycles, was essentially determined as well. Improving the results of DeBiasio, Gyárfás, Krueger, Ruszinkó, and Sárközy, in this paper we determine asymptotically the 4 -colour bipartite Ramsey number of paths and cycles. We also provide new upper bounds on the k -colour bipartite Ramsey numbers of paths and cycles which are close to being tight.
| Type: | Article |
|---|---|
| Title: | Multicolour Bipartite Ramsey Number of Paths |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.37236/8458 |
| Publisher version: | https://doi.org/10.37236/8458 |
| Language: | English |
| Additional information: | Copyright © The authors. Released under the CC BY license (International 4.0). |
| 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/10107288 |
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