Extension from Precoloured Sets of Edges
Identifieur interne : 002165 ( Hal/Curation ); précédent : 002164; suivant : 002166Extension from Precoloured Sets of Edges
Auteurs : Katherine Edwards [États-Unis] ; Jan Van Den Heuvel [Royaume-Uni] ; Ross J. Kang [Pays-Bas] ; Jean-Sébastien Sereni [France]Source :
English descriptors
Abstract
We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree Δ. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? For simple graphs, we conjecture that it is guaranteed as long as the predefined set of available colours has cardinality Δ+1. This turns out to be related to the notorious list colouring conjecture and other classic notions of choosability.
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<front><div type="abstract" xml:lang="en">We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree Δ. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? For simple graphs, we conjecture that it is guaranteed as long as the predefined set of available colours has cardinality Δ+1. This turns out to be related to the notorious list colouring conjecture and other classic notions of choosability.</div>
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<author role="aut"><persName><forename type="first">Jan</forename>
<surname>Van Den Heuvel</surname>
</persName>
<idno type="halAuthorId">178357</idno>
<affiliation ref="#struct-34676"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Ross J.</forename>
<surname>Kang</surname>
</persName>
<idno type="halAuthorId">97952</idno>
<affiliation ref="#struct-261281"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Jean-Sébastien</forename>
<surname>Sereni</surname>
</persName>
<email>Jean-Sebastien.Sereni@loria.fr</email>
<idno type="halAuthorId">808750</idno>
<affiliation ref="#struct-205125"></affiliation>
</author>
</analytic>
<monogr><imprint><date type="datePub">2014</date>
</imprint>
<authority type="institution">Loria & Inria Grand Est</authority>
</monogr>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><keywords scheme="author"><term xml:lang="en">mutligraph</term>
<term xml:lang="en">precolouring</term>
<term xml:lang="en">edge-colouring</term>
<term xml:lang="en">colouring extension</term>
</keywords>
<classCode scheme="classification">05C15</classCode>
<classCode scheme="halDomain" n="math.math-co">Mathematics [math]/Combinatorics [math.CO]</classCode>
<classCode scheme="halTypology" n="REPORT">Reports</classCode>
</textClass>
<abstract xml:lang="en">We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree Δ. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? For simple graphs, we conjecture that it is guaranteed as long as the predefined set of available colours has cardinality Δ+1. This turns out to be related to the notorious list colouring conjecture and other classic notions of choosability.</abstract>
</profileDesc>
</hal>
</record>
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