On almost-regular edge colourings of hypergraphs
type: Item
instance of: scholarly article
title: On almost-regular edge colourings of hypergraphs
zbMATH Open document ID: 1351.05071
published in: The Electronic Journal of Combinatorics
publication date: 2016-12-06T00:00:00Z
full work available at URL: v23i4p7
review text: Summary: We prove that if \(\mathcal{H}=(V(\mathcal{H}),\mathcal{E}(\mathcal{H}))\) is a hypergraph, \(\gamma\) is an edge colouring of \(\mathcal{H}\), and \(S\subseteq V(\mathcal{H})\) such that any permutation of \(S\) is an automorphism of \(\mathcal{H}\), then there exists a permutation \(\pi\) of \(\mathcal{E}(\mathcal{H})\) such that \(|\pi(E)|=|E|\) and \(\pi(E)\backslash S=E\backslash S\) for each \(E\in\mathcal{H}(\mathcal{H})\), and such that the edge colouring \(\gamma'\) of \(\mathcal{H}\) given by \(\gamma'(E)=\gamma(\pi^{-1}(E))\) for each \(E\in\mathcal{E}(\mathcal{H})\) is almost regular on \(S\). The proof is short and elementary. We show that a number of known results, such as Baranyai's theorem on almost-regular edge colourings of complete \(k\)-uniform hypergraphs, are easy corollaries of this theorem.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 6661359
zbMATH Keywords: hypergraphs
zbMATH Keywords: edge colouring
author: Darryn Bryant
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6661359