InforLorV4, Hal, Corpus, bibRecord, 002165

Extension from Precoloured Sets of Edges

Identifieur interne : 002165 ( Hal/Corpus ); précédent : 002164; suivant : 002166

Extension from Precoloured Sets of Edges

Auteurs : Katherine Edwards ; Jan Van Den Heuvel ; Ross J. Kang ; Jean-Sébastien Sereni

Source :

RBID : Hal:hal-01024843

English descriptors

mix :
- colouring extension, edge-colouring, mutligraph, precolouring.

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.

Url:

https://hal.archives-ouvertes.fr/hal-01024843

Links to Exploration step

Hal:hal-01024843

Le document en format XML

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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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<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>
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Extension from Precoloured Sets of Edges

Extension from Precoloured Sets of Edges

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