Ramsey numbers for bipartite graphs with small bandwidth

Author(s)

Mota, G. O. ; Sarkoezy, G. N. ; Schacht, M. ; Taraz, A.

• Document type: Journal article
• Source: EUROPEAN JOURNAL OF COMBINATORICS; v. 48, p. 12-pg., 2015-08-01.

Abstract

We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. In particular we determine asymptotically the two and three color Ramsey numbers for grid graphs. More generally, we determine asymptotically the two color Ramsey number for bipartite graphs with small bandwidth and bounded maximum degree and the three color Ramsey number for such graphs with the additional assumption that the bipartite graph is balanced. (C) 2015 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 09/06294-0 - Asymptotic combinatorics of sparse structures and regularity
• Grantee: Guilherme Oliveira Mota
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 12/00036-2 - Asymptotic combinatorics of sparse structures and regularity
• Grantee: Guilherme Oliveira Mota
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate