Chromatic index of simple hypergraphs
type: Item
instance of: scholarly article
title: Chromatic index of simple hypergraphs
zbMATH Open document ID: 1452.05072
author: Guo-Hui Zhang
author: Brett Skinner
published in: Discrete Mathematics
publication date: 2020-10-08T00:00:00Z
review text: The authors consider the problem of edge coloring of simple hypergraphs. There is a very well-known conjecture given independly by \textit{C. Berge} [in: Combinatorial mathematics, Proc. 3rd Int. Conf., New York/ NY (USA) 1985, Ann. N. Y. Acad. Sci. 555, 40--44 (1989; Zbl 0726.05055)] and \textit{Z. Füredi} [Graphs Comb. 2, 89--92 (1986; Zbl 0589.05036)]. It says that \(\chi^\prime(H)\leq \Delta(H)+1\) for any simple hypergraph \(H\). The authors prove this conjecture for simple hypergraphs of degree at most 5. Moreover, they give a new upper bound on the chromatic index of the hypergraph \(H\), namely \(\chi^\prime(H)\leq \frac{7}{4}\Delta(H) - 1\). The paper gives a very nice contribution to the problem of hyperedge coloring.
reviewed by: Hanna Furmańczyk
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 7257922
zbMATH Keywords: chromatic index
zbMATH Keywords: simple hypergraphs
MaRDI profile type: Publication
full work available at URL: j.disc.2020.112087
OpenAlex ID: W3081266286
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DOI: 10.1016/J.DISC.2020.112087
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description: scientific article; zbMATH DE number 7257922