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Critical Extreme Points of the 2-Edge Connected Spannning Subgraph Polytope

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Integer Programming and Combinatorial Optimization (IPCO 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1610))

Abstract

In this paper we study the extreme points of the polytope P(G), the linear relaxation of the 2-edge connected spanning subgraph polytope of a graph G. We introduce a partial ordering on the extreme points of P(G) and give necessary conditions for a non-integer extreme point of P(G) to be minimal with respect to that ordering. We show that, if \( \bar x\) is a non-integer minimal extreme point of P(G), then G and \( \bar x\) can be reduced, by means of some reduction operations, to a graph G′ and an extreme point \( \bar x'\) of P(G′) where G′ and \( \bar x'\) satisfy some simple properties. As a consequence we obtain a characterization of the perfectly 2-edge connected graphs, the graphs for which the polytope P(G) is integral.

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Author information

Authors and Affiliations

  1. Équipe de Combinatoire, UF9 921, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France

    Jean Fonlupt

  2. Complexe Scientifique des Cézeaux, LIMOS, Université de Clermont II, 63177, Aubière Cedex, France

    Ali Ridha Mahjoub

Authors
  1. Jean Fonlupt
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  2. Ali Ridha Mahjoub
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Editor information

Editors and Affiliations

  1. GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard  & Gerhard J. Woeginger  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Fonlupt, J., Mahjoub, A.R. (1999). Critical Extreme Points of the 2-Edge Connected Spannning Subgraph Polytope. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_13

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  • DOI: https://doi.org/10.1007/3-540-48777-8_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66019-4

  • Online ISBN: 978-3-540-48777-7

  • eBook Packages: Springer Book Archive

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