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

Authors:
Jean Fonlupt;Ali Ridha Mahjoub
Affiliations:
-;-
Venue:
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Year:
1999

Citing 14
Cited 1

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