Paper Info
Title
Three-colored asymmetric bipartite Ramsey number of connected matchings and cycles.
Abstract
Guaranteed by Szemeredi's Regularity Lemma, a technique originated by Luczak is to reduce the problem of showing the existence of a monochromatic cycle to show the existence of a monochromatic matching in a component. So determining the Ramsey number of connected matchings is crucial in determining the Ramsey number of cycles. Let k,l,m be integers and r(k,l,m) be the minimum integer N such that for any red-blue-green coloring of KN,N, there is a red matching of size at least k in a component, or a blue matching of size at least l in a component, or a green matching of size at least m in a component. Bucic, Letzter, and Sudakov determined the exact value of r(k,l,l) and led to the asymptotic value of 3-colored bipartite Ramsey number of cycles (symmetric case). In this paper, we determine the exact value of r(k,l,m) completely. This answers a question of Bucic, Letzter, and Sudakov. The crucial part of the proof is the construction we give in Section 4. Applying the technique of Luczak, we obtain the asymptotic value of 3-colored bipartite Ramsey number of cycles for all asymmetric cases.
Year
DOI
Venue
2020
10.1002/jgt.22549
JOURNAL OF GRAPH THEORY
Keywords
DocType
Volume
bipartite Ramsey number,bipartite Ramsey number of cycles
Journal
95.0
Issue
ISSN
Citations 
SP3.0
0364-9024
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Zhidan Luo100.68
Yuejian Peng223.46