Extension from Precoloured Sets of Edges
Identifieur interne : 000E74 ( Main/Exploration ); précédent : 000E73; suivant : 000E75Extension 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.
Url:
Affiliations:
- France, Pays-Bas, Royaume-Uni, États-Unis
- Grand Est, Lorraine (région)
- Metz, Nancy
- Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 002165
- to stream Hal, to step Curation: 002165
- to stream Hal, to step Checkpoint: 000D39
- to stream Main, to step Merge: 000E76
- to stream Main, to step Curation: 000E74
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Extension from Precoloured Sets of Edges</title>
<author><name sortKey="Edwards, Katherine" sort="Edwards, Katherine" uniqKey="Edwards K" first="Katherine" last="Edwards">Katherine Edwards</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-36756" status="VALID"><orgName>Department of Computer Science</orgName>
<desc><address><addrLine>Princeton University 35 Olden Street, Princeton, NJ 08540-5233</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.cs.princeton.edu/</ref>
</desc>
<listRelation><relation active="#struct-46584" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-46584" type="direct"><org type="institution" xml:id="struct-46584" status="VALID"><orgName>Princeton University [Pinceton]</orgName>
<desc><address><addrLine>Princeton University Princeton, NJ 08544 USA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.princeton.edu/main/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Van Den Heuvel, Jan" sort="Van Den Heuvel, Jan" uniqKey="Van Den Heuvel J" first="Jan" last="Van Den Heuvel">Jan Van Den Heuvel</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-34676" status="VALID"><orgName>Department Mathematics [London]</orgName>
<orgName type="acronym">LSE</orgName>
<desc><address><addrLine>Columbia House London School of Economics Houghton Street London WC2A 2AE, UK</addrLine>
<country key="GB"></country>
</address>
<ref type="url">http://www2.lse.ac.uk/maths/home.aspx</ref>
</desc>
<listRelation><relation active="#struct-10720" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-10720" type="direct"><org type="institution" xml:id="struct-10720" status="VALID"><orgName>London School of Economics</orgName>
<orgName type="acronym">LSE</orgName>
<desc><address><addrLine>LSE, Houghton Street, London WC2A 2AE, UK</addrLine>
<country key="GB"></country>
</address>
<ref type="url">http://econ.lse.ac.uk/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Royaume-Uni</country>
</affiliation>
</author>
<author><name sortKey="Kang, Ross J" sort="Kang, Ross J" uniqKey="Kang R" first="Ross J." last="Kang">Ross J. Kang</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-261281" status="INCOMING"><orgName>Applied Stochastics</orgName>
<orgName type="acronym">IMAPP</orgName>
<desc><address><country key="NL"></country>
</address>
</desc>
<listRelation><relation active="#struct-300856" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300856" type="direct"><org type="institution" xml:id="struct-300856" status="VALID"><orgName>Radboud university [Nijmegen]</orgName>
<desc><address><addrLine>Comeniuslaan 4, 6525 HP Nijmegen</addrLine>
<country key="NL"></country>
</address>
<ref type="url">http://www.ru.nl/english/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Pays-Bas</country>
</affiliation>
</author>
<author><name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-205125" status="VALID"><idno type="RNSR">200818291B</idno>
<orgName>Knowledge representation, reasonning</orgName>
<orgName type="acronym">ORPAILLEUR</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/orpailleur</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423086" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423086" type="direct"><org type="department" xml:id="struct-423086" status="VALID"><orgName>Department of Natural Language Processing & Knowledge Discovery</orgName>
<orgName type="acronym">LORIA - NLPKD</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/Knowledge-and-Language-Management</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-01024843</idno>
<idno type="halId">hal-01024843</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-01024843</idno>
<idno type="url">https://hal.archives-ouvertes.fr/hal-01024843</idno>
<date when="2014">2014</date>
<idno type="wicri:Area/Hal/Corpus">002165</idno>
<idno type="wicri:Area/Hal/Curation">002165</idno>
<idno type="wicri:Area/Hal/Checkpoint">000D39</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000D39</idno>
<idno type="wicri:Area/Main/Merge">000E76</idno>
<idno type="wicri:Area/Main/Curation">000E74</idno>
<idno type="wicri:Area/Main/Exploration">000E74</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Extension from Precoloured Sets of Edges</title>
<author><name sortKey="Edwards, Katherine" sort="Edwards, Katherine" uniqKey="Edwards K" first="Katherine" last="Edwards">Katherine Edwards</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-36756" status="VALID"><orgName>Department of Computer Science</orgName>
<desc><address><addrLine>Princeton University 35 Olden Street, Princeton, NJ 08540-5233</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.cs.princeton.edu/</ref>
</desc>
<listRelation><relation active="#struct-46584" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-46584" type="direct"><org type="institution" xml:id="struct-46584" status="VALID"><orgName>Princeton University [Pinceton]</orgName>
<desc><address><addrLine>Princeton University Princeton, NJ 08544 USA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.princeton.edu/main/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Van Den Heuvel, Jan" sort="Van Den Heuvel, Jan" uniqKey="Van Den Heuvel J" first="Jan" last="Van Den Heuvel">Jan Van Den Heuvel</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-34676" status="VALID"><orgName>Department Mathematics [London]</orgName>
<orgName type="acronym">LSE</orgName>
<desc><address><addrLine>Columbia House London School of Economics Houghton Street London WC2A 2AE, UK</addrLine>
<country key="GB"></country>
</address>
<ref type="url">http://www2.lse.ac.uk/maths/home.aspx</ref>
</desc>
<listRelation><relation active="#struct-10720" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-10720" type="direct"><org type="institution" xml:id="struct-10720" status="VALID"><orgName>London School of Economics</orgName>
<orgName type="acronym">LSE</orgName>
<desc><address><addrLine>LSE, Houghton Street, London WC2A 2AE, UK</addrLine>
<country key="GB"></country>
</address>
<ref type="url">http://econ.lse.ac.uk/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Royaume-Uni</country>
</affiliation>
</author>
<author><name sortKey="Kang, Ross J" sort="Kang, Ross J" uniqKey="Kang R" first="Ross J." last="Kang">Ross J. Kang</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-261281" status="INCOMING"><orgName>Applied Stochastics</orgName>
<orgName type="acronym">IMAPP</orgName>
<desc><address><country key="NL"></country>
</address>
</desc>
<listRelation><relation active="#struct-300856" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-300856" type="direct"><org type="institution" xml:id="struct-300856" status="VALID"><orgName>Radboud university [Nijmegen]</orgName>
<desc><address><addrLine>Comeniuslaan 4, 6525 HP Nijmegen</addrLine>
<country key="NL"></country>
</address>
<ref type="url">http://www.ru.nl/english/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Pays-Bas</country>
</affiliation>
</author>
<author><name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-205125" status="VALID"><idno type="RNSR">200818291B</idno>
<orgName>Knowledge representation, reasonning</orgName>
<orgName type="acronym">ORPAILLEUR</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/orpailleur</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423086" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423086" type="direct"><org type="department" xml:id="struct-423086" status="VALID"><orgName>Department of Natural Language Processing & Knowledge Discovery</orgName>
<orgName type="acronym">LORIA - NLPKD</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/Knowledge-and-Language-Management</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</analytic>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>colouring extension</term>
<term>edge-colouring</term>
<term>mutligraph</term>
<term>precolouring</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<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>
</front>
</TEI>
<affiliations><list><country><li>France</li>
<li>Pays-Bas</li>
<li>Royaume-Uni</li>
<li>États-Unis</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="États-Unis"><noRegion><name sortKey="Edwards, Katherine" sort="Edwards, Katherine" uniqKey="Edwards K" first="Katherine" last="Edwards">Katherine Edwards</name>
</noRegion>
</country>
<country name="Royaume-Uni"><noRegion><name sortKey="Van Den Heuvel, Jan" sort="Van Den Heuvel, Jan" uniqKey="Van Den Heuvel J" first="Jan" last="Van Den Heuvel">Jan Van Den Heuvel</name>
</noRegion>
</country>
<country name="Pays-Bas"><noRegion><name sortKey="Kang, Ross J" sort="Kang, Ross J" uniqKey="Kang R" first="Ross J." last="Kang">Ross J. Kang</name>
</noRegion>
</country>
<country name="France"><region name="Grand Est"><name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name>
</region>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000E74 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000E74 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= Main |étape= Exploration |type= RBID |clé= Hal:hal-01024843 |texte= Extension from Precoloured Sets of Edges }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |