Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777385 | European Journal of Combinatorics | 2017 | 10 Pages |
Abstract
We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that (kâ1)n+o(n)⩽Rk(Pn)⩽Rk(Cn)⩽kn+o(n). The upper bound was recently improved by Sárközy who showed that Rk(Cn)⩽kâk16k3+1n+o(n). Here we show Rk(Cn)⩽(kâ14)n+o(n), obtaining the first improvement to the coefficient of the linear term by an absolute constant.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
E. Davies, M. Jenssen, B. Roberts,