Rainbow numbers for matchings and complete graphs
type: Item
instance of: scholarly article
title: Rainbow numbers for matchings and complete graphs
zbMATH Open document ID: 1053.05053
author: Ingo Schiermeyer
published in: Discrete Mathematics
publication date: 2004-10-01T00:00:00Z
review text: If \(H\) is a graph and \(n\) is a positive integer then the rainbow number \(\text{rb}(n,H)\) is defined as the minimum number of colours that must be used to colour the edges of \(K_n\) in such a way that the edges of a copy of \(H\) in \(K_n\) have pairwise different colours (such a copy of \(H\) is called rainbow or totally multicoloured). The rainbow numbers \(\text{rb}(n,K_k)\) for all \(n\geq k\geq 4\) and the rainbow numbers \(\text{rb}(n,k{K_2})\) for all \(k\geq 2\) and \(n\geq 3k+3\) are determined. A short overview of earlier results and a relationship to some results from extremal graph theory are presented as well.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 2105623
zbMATH Keywords: edge colouring
zbMATH Keywords: rainbow subgraph
zbMATH Keywords: rainbow number
reviewed by: Gabriel Semanišin
MaRDI profile type: Publication
full work available at URL: j.disc.2003.11.057
OpenAlex ID: W2033759535
cites work: On a conjecture of erdöus, simonovits, and sós concerning anti‐Ramsey theorems
cites work: Q5422499
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cites work: Q4075490
cites work: On the Erdős–Simonovits–Sós Conjecture about the Anti-Ramsey Number of a Cycle
cites work: On restricted colourings of \(K_ n\)
DOI: 10.1016/J.DISC.2003.11.057
description: scientific article; zbMATH DE number 2105623