Ramsey numbers for sets of small graphs
type: Item
instance of: scholarly article
title: Ramsey numbers for sets of small graphs
zbMATH Open document ID: 0797.05061
DOI: 10.1016/0012-365X(94)90146-5
author: Holger Brandes
author: Heiko Harborth
author: Hans-Dietrich O. F. Gronau
author: Christian Schwahn
published in: Discrete Mathematics
publication date: 1994-10-10T00:00:00Z
review text: Define the Ramsey number for sets of graphs \(r=r(G_ 1-G_ 2-\cdots- G_ m,H_ 1-H_ 2-\cdots-H_ n)\) to be the smallest \(r\), such that every 2-coloring of the edges of the complete graph \(K_ r\) contains a subgraph \(G_ i\) with all edges of one color, or a subgraph \(H_ i\) with all edges of the other color. The authors show all 508 Ramsey numbers: (i) for all sets of graphs with at most \(H\) vertices (198), (ii) in the diagonal case \((m=n\), \(G_ i=H_ i)\) for all pairs of graphs, one with at most 4 and one with 5 vertices (65), (iii) in the diagonal case for all sets of graphs with 5 vertices (245).
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 562649
zbMATH Keywords: Ramsey number
reviewed by: Jiahai Kan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 562649