3‐Color bipartite Ramsey number of cycles and paths. Issue 4 (7th May 2019)

• Record Type: Journal Article
• Authors: Bucić, Matija; Letzter, Shoham; Sudakov, Benny
• Is Part Of: Journal of graph theory. Volume 92:Issue 4(2019)
• Page Start: 445
• Page End: 459
• Publication Date: 2019-05-07
• Subjects: bipartite Ramsey number -- cycle Ramsey number -- connected matchings -- path Ramsey number; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22463
• Languages: English
• ISSNs: 0364-9024

Abstract

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.