Bull-Reducible Berge Graphs are Perfect
Identifieur interne : 009682 ( Main/Exploration ); précédent : 009681; suivant : 009683Bull-Reducible Berge Graphs are Perfect
Auteurs : Hazel Everett [France] ; Celina De Figueiredo ; Sulamita Klein ; Bruce ReedSource :
English descriptors
Abstract
Berge's well known SPGC (Strong Perfect Graph Conjecture) states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is bull-reducible if no vertex is in two bulls. We prove that every bull-reducible Berge graph is perfect and we exhibit a polynomial-time recognition algorithm for bull-reducible Berge graphs.
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Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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xml:lang="en">Berge's well known SPGC (Strong Perfect Graph Conjecture) states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is bull-reducible if no vertex is in two bulls. We prove that every bull-reducible Berge graph is perfect and we exhibit a polynomial-time recognition algorithm for bull-reducible Berge graphs.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><noCountry><name sortKey="De Figueiredo, Celina" sort="De Figueiredo, Celina" uniqKey="De Figueiredo C" first="Celina" last="De Figueiredo">Celina De Figueiredo</name><name sortKey="Klein, Sulamita" sort="Klein, Sulamita" uniqKey="Klein S" first="Sulamita" last="Klein">Sulamita Klein</name><name sortKey="Reed, Bruce" sort="Reed, Bruce" uniqKey="Reed B" first="Bruce" last="Reed">Bruce Reed</name></noCountry><country name="France"><region name="Grand Est"><name sortKey="Everett, Hazel" sort="Everett, Hazel" uniqKey="Everett H" first="Hazel" last="Everett">Hazel Everett</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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