Voloshin's colourings of \(P_{3}\)-designs
type: Item
instance of: scholarly article
title: Voloshin's colourings of \(P_{3}\)-designs
zbMATH Open document ID: 1031.05048
DOI: 10.1016/S0012-365X(03)00104-3
author: Lucia Gionfriddo
published in: Discrete Mathematics
publication date: 2004-02-02T00:00:00Z
review text: The mixed hypergraph coloring problem is to color the vertex set of a hypergraph in such a way that some hyperedges (called \(\mathcal C\)-edges) contain at least two vertices in a common color and some (called \(\mathcal D\)-edges) contain vertices in at least two different colors. This general problem was introduced by \textit{V. I. Voloshin} [Coloring mixed hypergraphs: theory, algorithms and applications (Fields Institute Monographs. 17. Providence) (2002; Zbl 1001.05003)]. The present author considers the special case of \(P_3\) designs, where he regards each block both as a \(\mathcal C\)-edge and a \(\mathcal D\)-edge. In other words, he is looking for colorings of such designs such that each block contains exactly two different colors. He constructs several \(P_3\)-designs having particular properties of mixed hypergraphs like broken spectrum, equal lower and upper chromatic number and others.
reviewed by: Benjamin Doerr
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 2035869
zbMATH Keywords: hypergraph coloring
zbMATH Keywords: mixed hypergraphs
MaRDI profile type: Publication
cites work: Bicoloring Steiner triple systems
cites work: Q4256358
cites work: Q4288120
cites work: The monochromatic block number
cites work: Upper chromatic number of Steiner triple and quadruple systems
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description: scientific article; zbMATH DE number 2035869