Show simple item record

dc.contributor.authorChristophe, J.en_US
dc.contributor.authorDewez, S.en_US
dc.contributor.authorDoignon, J-P.en_US
dc.contributor.authorFasbender, G.en_US
dc.contributor.authorGrégoire, P.en_US
dc.contributor.authorHuygens, D.en_US
dc.contributor.authorLabbé, M.en_US
dc.contributor.authorElloumi, S.en_US
dc.contributor.authorMélot, H.en_US
dc.contributor.authorYaman, H.en_US
dc.date.accessioned2016-02-08T10:06:50Z
dc.date.available2016-02-08T10:06:50Z
dc.date.issued2008en_US
dc.identifier.issn0028-3045
dc.identifier.urihttp://hdl.handle.net/11693/22943
dc.description.abstractOptimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph vertices, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tuples. By definition, the optimal linear inequalities correspond to the facets of this polytope. They are finite in number, are logically independent, and generate precisely all the linear inequalities valid on the class of graphs. The computer system GraPHedron, developed by some of the authors, is able to produce experimental data about such inequalities for a "small" number of vertices. It greatly helps in conjecturing optimal linear inequalities, which are then hopefully proved for any number of vertices. Two examples are investigated here for the class of connected graphs. First, all the optimal linear inequalities for the stability number and the number of edges are obtained. To this aim, a problem of Ore (1962) related to the Turán Theorem (1941) is solved. Second, several optimal inequalities are established for three invariants: the maximum degree, the irregularity, and the diameter.en_US
dc.language.isoEnglishen_US
dc.source.titleGraph invariantsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1002/net.20250en_US
dc.subjectPolytopeen_US
dc.subjectOptimal linear inequalitiesen_US
dc.subjectGraPHedronen_US
dc.titleLinear inequalities among graph invariants: using graPHedron to uncover optimal relationshipsen_US
dc.typeArticleen_US
dc.departmentDepartment of Industrial Engineering
dc.citation.spage287en_US
dc.citation.epage298en_US
dc.citation.volumeNumber52en_US
dc.citation.issueNumber4en_US
dc.identifier.doi10.1002/net.20250en_US
dc.publisherJohn Wiley & Sonsen_US
dc.identifier.eissn1097-0037


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record