On the path-complete bipartite Ramsey number
type: Item
instance of: scholarly article
title: On the path-complete bipartite Ramsey number
zbMATH Open document ID: 0692.05046
DOI: 10.1016/0012-365X(89)90090-3
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: An upper bound for the path-complete bipartite graph Ramsey number \(r(P_ k,K_{n,m})\leq n+m+k-2\) is proved. An immediate corollary is the exact result \(r(P_ k,K_{n,m})=n+m+k-2\) for \(n\equiv m\equiv 1 mod(k- 1),\) since \((n+m-3)/(k-1)\) disjoint copies of a \(K_{k-1}\) does not contain a \(P_ k\) and the complementary graph does not contain a \(K_{n,m}\). Clever use of a minimal counterexample type of argument gives a relatively short proof of the main inequality.
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 4132202
zbMATH Keywords: path
zbMATH Keywords: bipartite graph Ramsey number
author: Roland Häggkvist
MaRDI profile type: Publication
cites work: Q4044602
cites work: Path-star Ramsey numbers
description: scientific article; zbMATH DE number 4132202