k-tuple chromatic number of the cartesian product of graphs
Identifieur interne : 005456 ( Hal/Curation ); précédent : 005455; suivant : 005457k-tuple chromatic number of the cartesian product of graphs
Auteurs : Flavia Bonomo [Argentine] ; Ivo Koch [Argentine] ; Pablo Torres [Argentine] ; Mario Valencia-Pabon [France]Source :
English descriptors
- mix :
Abstract
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χ k (G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(GH) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (GH) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families such that, for any k ≥ 1, the k-tuple chromatic number of their cartesian product is equal to the maximum k-tuple chromatic number of its factors.
Url:
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: Pour aller vers cette notice dans l'étape Curation :005456
Links to Exploration step
Hal:hal-01103534Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">k-tuple chromatic number of the cartesian product of graphs</title><author><name sortKey="Bonomo, Flavia" sort="Bonomo, Flavia" uniqKey="Bonomo F" first="Flavia" last="Bonomo">Flavia Bonomo</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-151993" status="VALID"><orgName>Departamento de Computación</orgName><orgName type="acronym">DC</orgName><desc><address><addrLine>Ciudad Universitaria, Pabellon I, Buenos Aires, 1428</addrLine><country key="AR"></country></address><ref type="url">http://dc.uba.ar</ref></desc><listRelation><relation active="#struct-338192" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-338192" type="direct"><org type="institution" xml:id="struct-338192" status="INCOMING"><orgName>Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Argentine</country></affiliation></author><author><name sortKey="Koch, Ivo" sort="Koch, Ivo" uniqKey="Koch I" first="Ivo" last="Koch">Ivo Koch</name><affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-410322" status="VALID"><orgName>Universidad Nacional de General Sarmiento [Los Polvorines, Buenos Aires]</orgName><orgName type="acronym">UNGS</orgName><desc><address><addrLine>Juan María Gutiérrez 1150, 1613 Los Polvorines, Buenos Aires, Argentina</addrLine><country key="AR"></country></address></desc></hal:affiliation><country>Argentine</country></affiliation></author><author><name sortKey="Torres, Pablo" sort="Torres, Pablo" uniqKey="Torres P" first="Pablo" last="Torres">Pablo Torres</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-92878" status="VALID"><orgName>Consejo Nacional de Investigaciones Científicas y Técnicas</orgName><orgName type="acronym">CONICET</orgName><desc><address><addrLine>Avda. Rivadavia 1917 - CP C1033AAJ - Cdad. de Buenos Aires</addrLine><country key="AR"></country></address><ref type="url">http://www.conicet.gov.ar/</ref></desc><listRelation><relation active="#struct-305291" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-305291" type="direct"><org type="institution" xml:id="struct-305291" status="INCOMING"><orgName>University of Buenos Aires</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Argentine</country></affiliation></author><author><name sortKey="Valencia Pabon, Mario" sort="Valencia Pabon, Mario" uniqKey="Valencia Pabon M" first="Mario" last="Valencia-Pabon">Mario Valencia-Pabon</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-01103534</idno><idno type="halId">hal-01103534</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-01103534</idno><idno type="url">https://hal.archives-ouvertes.fr/hal-01103534</idno><date when="2014-11-22">2014-11-22</date><idno type="wicri:Area/Hal/Corpus">005456</idno><idno type="wicri:Area/Hal/Curation">005456</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">k-tuple chromatic number of the cartesian product of graphs</title><author><name sortKey="Bonomo, Flavia" sort="Bonomo, Flavia" uniqKey="Bonomo F" first="Flavia" last="Bonomo">Flavia Bonomo</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-151993" status="VALID"><orgName>Departamento de Computación</orgName><orgName type="acronym">DC</orgName><desc><address><addrLine>Ciudad Universitaria, Pabellon I, Buenos Aires, 1428</addrLine><country key="AR"></country></address><ref type="url">http://dc.uba.ar</ref></desc><listRelation><relation active="#struct-338192" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-338192" type="direct"><org type="institution" xml:id="struct-338192" status="INCOMING"><orgName>Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Argentine</country></affiliation></author><author><name sortKey="Koch, Ivo" sort="Koch, Ivo" uniqKey="Koch I" first="Ivo" last="Koch">Ivo Koch</name><affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-410322" status="VALID"><orgName>Universidad Nacional de General Sarmiento [Los Polvorines, Buenos Aires]</orgName><orgName type="acronym">UNGS</orgName><desc><address><addrLine>Juan María Gutiérrez 1150, 1613 Los Polvorines, Buenos Aires, Argentina</addrLine><country key="AR"></country></address></desc></hal:affiliation><country>Argentine</country></affiliation></author><author><name sortKey="Torres, Pablo" sort="Torres, Pablo" uniqKey="Torres P" first="Pablo" last="Torres">Pablo Torres</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-92878" status="VALID"><orgName>Consejo Nacional de Investigaciones Científicas y Técnicas</orgName><orgName type="acronym">CONICET</orgName><desc><address><addrLine>Avda. Rivadavia 1917 - CP C1033AAJ - Cdad. de Buenos Aires</addrLine><country key="AR"></country></address><ref type="url">http://www.conicet.gov.ar/</ref></desc><listRelation><relation active="#struct-305291" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-305291" type="direct"><org type="institution" xml:id="struct-305291" status="INCOMING"><orgName>University of Buenos Aires</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Argentine</country></affiliation></author><author><name sortKey="Valencia Pabon, Mario" sort="Valencia Pabon, Mario" uniqKey="Valencia Pabon M" first="Mario" last="Valencia-Pabon">Mario Valencia-Pabon</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>Cartesian product of graphs</term><term>Cayley graphs</term><term>Hom-idempotent graphs</term><term>Kneser graphs</term><term>k-tuple colorings</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χ k (G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(GH) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (GH) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families such that, for any k ≥ 1, the k-tuple chromatic number of their cartesian product is equal to the maximum k-tuple chromatic number of its factors.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">k-tuple chromatic number of the cartesian product of graphs</title><author role="aut"><persName><forename type="first">Flavia</forename><surname>Bonomo</surname></persName><email></email><idno type="halauthor">482810</idno><affiliation ref="#struct-151993"></affiliation><affiliation ref="#struct-92878"></affiliation></author><author role="aut"><persName><forename type="first">Ivo</forename><surname>Koch</surname></persName><email></email><idno type="halauthor">1116413</idno><affiliation ref="#struct-410322"></affiliation></author><author role="aut"><persName><forename type="first">Pablo</forename><surname>Torres</surname></persName><email></email><idno type="halauthor">1116414</idno><affiliation ref="#struct-92878"></affiliation><affiliation ref="#struct-410323"></affiliation></author><author role="aut"><persName><forename type="first">Mario</forename><surname>Valencia-Pabon</surname></persName><email></email><idno type="halauthor">111523</idno><affiliation ref="#struct-205125"></affiliation><affiliation ref="#struct-994"></affiliation></author><editor role="depositor"><persName><forename>Mario</forename><surname>Valencia</surname></persName><email>valencia@lipn.univ-paris13.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2015-01-14 21:24:38</date><date type="whenWritten">2014-11-22</date><date type="whenModified">2015-09-22 01:12:12</date><date type="whenReleased">2015-01-15 09:02:38</date><date type="whenProduced">2014-11-22</date><date type="whenEndEmbargoed">2015-01-14</date><ref type="file" target="https://hal.archives-ouvertes.fr/hal-01103534/document"><date notBefore="2015-01-14"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.archives-ouvertes.fr/hal-01103534/file/cartesian-prod-multicol-ext-v0.pdf"><date notBefore="2015-01-14"></date></ref></edition><respStmt><resp>contributor</resp><name key="306281"><persName><forename>Mario</forename><surname>Valencia</surname></persName><email>valencia@lipn.univ-paris13.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-01103534</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-01103534</idno><idno type="halBibtex">bonomo:hal-01103534</idno><idno type="halRefHtml">2014</idno><idno type="halRef">2014</idno></publicationStmt><seriesStmt><idno type="stamp" n="UNIV-PARIS13">Université Paris-Nord - Paris XIII</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA-TALC" p="LORIA">Traitement automatique des langues et des connaissances</idno><idno type="stamp" n="LIPN" p="UNIV-PARIS13">Laboratoire d'Informatique de Paris-Nord</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno></seriesStmt><notesStmt></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">k-tuple chromatic number of the cartesian product of graphs</title><author role="aut"><persName><forename type="first">Flavia</forename><surname>Bonomo</surname></persName><idno type="halAuthorId">482810</idno><affiliation ref="#struct-151993"></affiliation><affiliation ref="#struct-92878"></affiliation></author><author role="aut"><persName><forename type="first">Ivo</forename><surname>Koch</surname></persName><idno type="halAuthorId">1116413</idno><affiliation ref="#struct-410322"></affiliation></author><author role="aut"><persName><forename type="first">Pablo</forename><surname>Torres</surname></persName><idno type="halAuthorId">1116414</idno><affiliation ref="#struct-92878"></affiliation><affiliation ref="#struct-410323"></affiliation></author><author role="aut"><persName><forename type="first">Mario</forename><surname>Valencia-Pabon</surname></persName><idno type="halAuthorId">111523</idno><affiliation ref="#struct-205125"></affiliation><affiliation ref="#struct-994"></affiliation></author></analytic><monogr><imprint></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">Hom-idempotent graphs</term><term xml:lang="en">Cartesian product of graphs</term><term xml:lang="en">Cayley graphs</term><term xml:lang="en">Kneser graphs</term><term xml:lang="en">k-tuple colorings</term></keywords><classCode scheme="halDomain" n="math">Mathematics [math]</classCode><classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode></textClass><abstract xml:lang="en">A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χ k (G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(GH) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (GH) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families such that, for any k ≥ 1, the k-tuple chromatic number of their cartesian product is equal to the maximum k-tuple chromatic number of its factors.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 005456 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Curation/biblio.hfd -nk 005456 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Hal
|étape= Curation
|type= RBID
|clé= Hal:hal-01103534
|texte= k-tuple chromatic number of the cartesian product of graphs
}}
| This area was generated with Dilib version V0.6.33. |  |