On the Ramsey numbers r(G,nH) and r(nG,nH) when n is large
type: Item
instance of: scholarly article
title: On the Ramsey numbers r(G,nH) and r(nG,nH) when n is large
zbMATH Open document ID: 0621.05024
DOI: 10.1016/0012-365X(87)90053-7
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let G and H be graphs. The Ramsey number \(r(G,H)\) is the smallest number p so that, if the edges of the complete graph on p vertices are colored with orange and blue, then either there is a subgraph isomorphic to G with all of its edges colored orange or a subgraph isomorphic to H with all of its edges colored blue. This paper is concerned with graphs of the form nG, i.e. the graph consisting of n disjoint copies of G. Several results are proved including: Theorem 5.3: If k and h are fixed and n is sufficiently large, then: \[ r(nK_ k,nK_ h)=(k+h-1)n+r(K_{k- 1},K_{h-1})-2. \]
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 4006299
zbMATH Keywords: Ramsey number
zbMATH Keywords: disjoint copies
author: Stefan A. Burr
reviewed by: Jack E. Graver
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4006299