On the B-Continuity Property of Graphs
Identifieur interne : 003737 ( Hal/Curation ); précédent : 003736; suivant : 003738On the B-Continuity Property of Graphs
Auteurs : Dominique Barth [France] ; Johanne Cohen [France] ; Taoufik Faik [France]Source :
- Discrete Applied Mathematics [ 0166-218X ] ; 2007.
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Abstract
This paper deals with b-colorings of a graph G, that is, proper colorings in which for each color c, there exists at least one vertex colored by c such that its neighbors are colored by each other color. The b-chromatic number b(G) of a graph G is the maximum number of colors for which G has a b-coloring. It is easy to see that every graph G has a b-coloring using ?(G) colors. We say that G is b-continuous iff for each k, ?(G)less-than-or-equals, slantkless-than-or-equals, slantb(G), there exists a b-coloring with k colors. It is well known that not all graphs are b-continuous. We call b-spectrum Sb(G) of G to be the set of integers k for which there is a b-coloring of G by k colors. We show that for any finite integer set I, there exists a graph whose b-spectrum is I and we investigate the complexity of the problem of deciding whether a graph G is b-continuous, even if b-colorings using ?(G) and b(G) colors are given.
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DOI: 10.1016/j.dam.2007.04.011
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The b-chromatic number b(G) of a graph G is the maximum number of colors for which G has a b-coloring. It is easy to see that every graph G has a b-coloring using ?(G) colors. We say that G is b-continuous iff for each k, ?(G)less-than-or-equals, slantkless-than-or-equals, slantb(G), there exists a b-coloring with k colors. It is well known that not all graphs are b-continuous. We call b-spectrum Sb(G) of G to be the set of integers k for which there is a b-coloring of G by k colors. We show that for any finite integer set I, there exists a graph whose b-spectrum is I and we investigate the complexity of the problem of deciding whether a graph G is b-continuous, even if b-colorings using ?(G) and b(G) colors are given.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">On the B-Continuity Property of Graphs</title><author role="aut"><persName><forename type="first">Dominique</forename><surname>Barth</surname></persName><email></email><idno type="halauthor">131147</idno><affiliation ref="#struct-31978"></affiliation></author><author role="aut"><persName><forename type="first">Johanne</forename><surname>Cohen</surname></persName><email>Johanne.Cohen@loria.fr</email><idno type="idhal">johanne-cohen</idno><idno type="halauthor">92180</idno><affiliation ref="#struct-29797"></affiliation></author><author role="aut"><persName><forename type="first">Taoufik</forename><surname>Faik</surname></persName><email></email><idno type="halauthor">159279</idno><affiliation ref="#struct-2544"></affiliation></author><editor role="depositor"><persName><forename>Isabelle</forename><surname>Moudenner Cohen</surname></persName><email>Isabelle.Moudenner@prism.uvsq.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2007-01-23 11:56:40</date><date type="whenModified">2015-09-22 01:13:02</date><date type="whenReleased">2007-01-23 11:56:40</date><date type="whenProduced">2007</date></edition><respStmt><resp>contributor</resp><name key="115878"><persName><forename>Isabelle</forename><surname>Moudenner Cohen</surname></persName><email>Isabelle.Moudenner@prism.uvsq.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-00126001</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-00126001</idno><idno type="halBibtex">barth:hal-00126001</idno><idno type="halRefHtml">Discrete Applied Mathematics, Elsevier, 2007, 155 (13), pp.1761 - 1768. <10.1016/j.dam.2007.04.011></idno><idno type="halRef">Discrete Applied Mathematics, Elsevier, 2007, 155 (13), pp.1761 - 1768. <10.1016/j.dam.2007.04.011></idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="PRISM">Parallélisme, Réseaux, Systèmes d'information, Modélisation</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</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">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</idno><idno type="stamp" n="UMR8623">Laboratoire de Recherche en Informatique</idno><idno type="stamp" n="UVSQ">Université de Versailles Saint-Quentin-en-Yvelines</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno></seriesStmt><notesStmt><note type="audience" n="2">International</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">On the B-Continuity Property of Graphs</title><author role="aut"><persName><forename type="first">Dominique</forename><surname>Barth</surname></persName><idno type="halAuthorId">131147</idno><affiliation ref="#struct-31978"></affiliation></author><author role="aut"><persName><forename type="first">Johanne</forename><surname>Cohen</surname></persName><email>Johanne.Cohen@loria.fr</email><idno type="idHal">johanne-cohen</idno><idno type="halAuthorId">92180</idno><affiliation ref="#struct-29797"></affiliation></author><author role="aut"><persName><forename type="first">Taoufik</forename><surname>Faik</surname></persName><idno type="halAuthorId">159279</idno><affiliation ref="#struct-2544"></affiliation></author></analytic><monogr><idno type="halJournalId" status="VALID">12621</idno><idno type="issn">0166-218X</idno><title level="j">Discrete Applied Mathematics</title><imprint><publisher>Elsevier</publisher><biblScope unit="volume">155</biblScope><biblScope unit="issue">13</biblScope><biblScope unit="pp">1761 – 1768</biblScope><date type="datePub">2007</date></imprint></monogr><idno type="doi">10.1016/j.dam.2007.04.011</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">Complexity</term><term xml:lang="en">Graph</term><term xml:lang="en">Coloring</term><term xml:lang="en">B-Chromatic number</term></keywords><classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><abstract xml:lang="en">This paper deals with b-colorings of a graph G, that is, proper colorings in which for each color c, there exists at least one vertex colored by c such that its neighbors are colored by each other color. The b-chromatic number b(G) of a graph G is the maximum number of colors for which G has a b-coloring. It is easy to see that every graph G has a b-coloring using ?(G) colors. We say that G is b-continuous iff for each k, ?(G)less-than-or-equals, slantkless-than-or-equals, slantb(G), there exists a b-coloring with k colors. It is well known that not all graphs are b-continuous. We call b-spectrum Sb(G) of G to be the set of integers k for which there is a b-coloring of G by k colors. We show that for any finite integer set I, there exists a graph whose b-spectrum is I and we investigate the complexity of the problem of deciding whether a graph G is b-continuous, even if b-colorings using ?(G) and b(G) colors are given.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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