Multicolour bipartite ramsey number of paths

Matija Bucić, Shoham Letzter

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 KN,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.

Original languageEnglish (US)
Article numberP3.60
JournalElectronic Journal of Combinatorics
Volume26
Issue number3
DOIs
StatePublished - 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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