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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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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