A note on list arboricity
type: Item
instance of: scholarly article
title: A note on list arboricity
zbMATH Open document ID: 0895.05015
published in: Journal of Combinatorial Theory. Series B
publication date: 1998-09-06T00:00:00Z
review text: An analogue of the result by \textit{F. Galvin} [J. Comb. Theory, Ser. B 63, No. 1, 153-158 (1995; Zbl 0826.05026)] is proved for edge colorings of graphs. The result by Galvin asserts that for a bipartite graph the chromatic index and the list chromatic index are equal. In this note it is shown that if the edges of a graph \(G\) can be colored by \(k\) colors such that no circuit is monochromatic then for any assignment \(E\) of \(k\) colors \(E(e)\) to each edge \(e\) of \(G\) there is a coloring of the edges choosing colors from \(E(e)\) such that no circuit is monochromatic. The result is proved in a more general form for matroids which specializes to the above statement in case \(M\) is the graphical matroid of the graph \(G\).
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1154566
zbMATH Keywords: list coloring
zbMATH Keywords: arboricity
zbMATH Keywords: matroid
author: Paul Seymour
reviewed by: Volkmar Welker
MaRDI profile type: Publication
full work available at URL: jctb.1997.1784
OpenAlex ID: W1995121620
cites work: Transversals and matroid partition
cites work: The list chromatic index of a bipartite multigraph
cites work: Q5582910
DOI: 10.1006/JCTB.1997.1784
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description: scientific article; zbMATH DE number 1154566