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Critical extreme points of the 2-edge connected spanning subgraph polytope

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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 is a non-integer minimal extreme point of P(G), then G and can be reduced, by means of some reduction operations, to a graph G' and an extreme point of P(G') where G' and 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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Authors and Affiliations

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

    Jean Fonlupt

  2. LIMOS, CNRS UMR 6158, Université Blaise Pascal Clermont II, Complexe Scientifique des Cézeaux, 63177, Aubière Cedex, France

    A. Ridha Mahjoub

Authors
  1. Jean Fonlupt
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  2. A. Ridha Mahjoub
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Correspondence to A. Ridha Mahjoub.

Additional information

Received: May, 2004

Part of this work has been done while the first author was visiting the Research Institute for Discrete Mathematics, University of Bonn, Germany.

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Fonlupt, J., Mahjoub, A. Critical extreme points of the 2-edge connected spanning subgraph polytope. Math. Program. 105, 289–310 (2006). https://doi.org/10.1007/s10107-005-0654-8

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Mathematics Subject Classification (2000)