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.
@article{10_37236_8458,
author = {Matija Bucic and Shoham Letzter and Benny Sudakov},
title = {Multicolour bipartite {Ramsey} number of paths},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8458},
zbl = {1420.05113},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8458/}
}
TY - JOUR
AU - Matija Bucic
AU - Shoham Letzter
AU - Benny Sudakov
TI - Multicolour bipartite Ramsey number of paths
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8458/
DO - 10.37236/8458
ID - 10_37236_8458
ER -
%0 Journal Article
%A Matija Bucic
%A Shoham Letzter
%A Benny Sudakov
%T Multicolour bipartite Ramsey number of paths
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8458/
%R 10.37236/8458
%F 10_37236_8458
Matija Bucic; Shoham Letzter; Benny Sudakov. Multicolour bipartite Ramsey number of paths. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8458
