dc.contributor.author Balbuena Martínez, Maria Camino Teófila dc.contributor.author Fàbrega Canudas, José dc.contributor.author Fiol Mora, Miquel Àngel dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2014-03-12T12:00:55Z dc.date.available 2014-03-12T12:00:55Z dc.date.created 2013-12-05 dc.date.issued 2013-12-05 dc.identifier.citation Balbuena, M.; Fàbrega, J.; Fiol, M. Connectivity: properties and structure. A: "Handbook of Graph Theory, Second Edition". CRC Press Taylor & Francis Group, 2013, p. 234-257. dc.identifier.isbn 978-1-4398-8018-0 dc.identifier.uri http://hdl.handle.net/2117/22004 dc.description.abstract Connectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, such as Menger’s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson’s theorem about flows and Hall’s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and fault-tolerant interconnection or communication networks. Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66]. dc.format.extent 24 p. dc.language.iso eng dc.publisher CRC Press Taylor & Francis Group dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria dc.subject.lcsh Graph theory dc.subject.other Graph Theory dc.subject.other Connectivity dc.title Connectivity: properties and structure dc.type Part of book or chapter of book dc.subject.lemac Grafs, Teoria de dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.identifier.doi 10.1201/b16132 dc.description.peerreviewed Peer Reviewed dc.subject.ams 05C Graph theory dc.relation.publisherversion http://www.crcnetbase.com/doi/book/10.1201/b16132 dc.rights.access Open Access local.identifier.drac 13031238 dc.description.version Postprint (published version) local.citation.author Balbuena, M.; Fàbrega, J.; Fiol, M. local.citation.publicationName Handbook of Graph Theory, Second Edition local.citation.startingPage 234 local.citation.endingPage 257
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