Another View of Bipartite Ramsey Numbers

Another View of Bipartite Ramsey Numbers

For bipartite graphs F and H and a positive integer s, the s-bipartite Ramsey number BRs(F,H) of F and H is the smallest integer t with t ≥ s such that every red-blue coloring of Ks,t results in a red F or a blue H. We evaluate this number for all positive integers s when F = K2,2 and H ∈ {K2,3,K3,3...

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Bibliographic Details
Main Authors: Bi Zhenming, Chartrand Gary, Zhang Ping
Format: Article
Language:English
Published: Sciendo 2018-05-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
ramsey number
bipartite ramsey number
s-bipartite ramsey number
05c35
05c55
Online Access:https://doi.org/10.7151/dmgt.2034
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spelling doaj-a129ce71136a4480b26c2f73f29055672021-09-05T17:20:23ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922018-05-0138258760510.7151/dmgt.2034dmgt.2034Another View of Bipartite Ramsey NumbersBi Zhenming0Chartrand Gary1Zhang Ping2Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USADepartment of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USADepartment of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USAFor bipartite graphs F and H and a positive integer s, the s-bipartite Ramsey number BRs(F,H) of F and H is the smallest integer t with t ≥ s such that every red-blue coloring of Ks,t results in a red F or a blue H. We evaluate this number for all positive integers s when F = K2,2 and H ∈ {K2,3,K3,3}.https://doi.org/10.7151/dmgt.2034ramsey numberbipartite ramsey numbers-bipartite ramsey number05c3505c55
collection DOAJ
language English
format Article
sources DOAJ
author Bi Zhenming
Chartrand Gary
Zhang Ping
spellingShingle Bi Zhenming
Chartrand Gary
Zhang Ping
Another View of Bipartite Ramsey Numbers
Discussiones Mathematicae Graph Theory
ramsey number
bipartite ramsey number
s-bipartite ramsey number
05c35
05c55
author_facet Bi Zhenming
Chartrand Gary
Zhang Ping
author_sort Bi Zhenming
title Another View of Bipartite Ramsey Numbers
title_short Another View of Bipartite Ramsey Numbers
title_full Another View of Bipartite Ramsey Numbers
title_fullStr Another View of Bipartite Ramsey Numbers
title_full_unstemmed Another View of Bipartite Ramsey Numbers
title_sort another view of bipartite ramsey numbers
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2018-05-01
description For bipartite graphs F and H and a positive integer s, the s-bipartite Ramsey number BRs(F,H) of F and H is the smallest integer t with t ≥ s such that every red-blue coloring of Ks,t results in a red F or a blue H. We evaluate this number for all positive integers s when F = K2,2 and H ∈ {K2,3,K3,3}.
topic ramsey number
bipartite ramsey number
s-bipartite ramsey number
05c35
05c55
url https://doi.org/10.7151/dmgt.2034
work_keys_str_mv AT bizhenming anotherviewofbipartiteramseynumbers
AT chartrandgary anotherviewofbipartiteramseynumbers
AT zhangping anotherviewofbipartiteramseynumbers
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