3-Color bipartite Ramsey number of cycles and paths

Matija Bucić; Shoham Letzter; Benny Sudakov

doi:10.1002/jgt.22463

3-Color bipartite Ramsey number of cycles and paths

Matija Bucić, Shoham Letzter, Benny Sudakov

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The k-color bipartite Ramsey number of a bipartite graph H is the least integer n for which every k-edge-colored 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-color Ramsey number of paths. In this paper we determine asymptotically the 3-color bipartite Ramsey number of paths and (even) cycles.

Original language	English (US)
Pages (from-to)	445-459
Number of pages	15
Journal	Journal of Graph Theory
Volume	92
Issue number	4
DOIs	https://doi.org/10.1002/jgt.22463
State	Published - Dec 1 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

bipartite Ramsey number
connected matchings
cycle Ramsey number
path Ramsey number

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10.1002/jgt.22463

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keywords = "bipartite Ramsey number, connected matchings, cycle Ramsey number, path Ramsey number",

author = "Matija Buci{\'c} and Shoham Letzter and Benny Sudakov",

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AU - Bucić, Matija

AU - Letzter, Shoham

AU - Sudakov, Benny

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N2 - The k-color bipartite Ramsey number of a bipartite graph H is the least integer n for which every k-edge-colored 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-color Ramsey number of paths. In this paper we determine asymptotically the 3-color bipartite Ramsey number of paths and (even) cycles.

AB - The k-color bipartite Ramsey number of a bipartite graph H is the least integer n for which every k-edge-colored 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-color Ramsey number of paths. In this paper we determine asymptotically the 3-color bipartite Ramsey number of paths and (even) cycles.

KW - bipartite Ramsey number

KW - connected matchings

KW - cycle Ramsey number

KW - path Ramsey number

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JF - Journal of Graph Theory

IS - 4

ER -

3-Color bipartite Ramsey number of cycles and paths

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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