Half integer extreme points in the linear relaxation of the 2-edge-connected subgraph polyhedron

F. Bendali () and J. Mailfert ()
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F. Bendali: Complexe Scientifique des Cézeaux
J. Mailfert: Complexe Scientifique des Cézeaux

Journal of Combinatorial Optimization, 2009, vol. 18, issue 1, No 1, 22 pages

Abstract: Abstract This paper studies the graphs for which the linear relaxation of the 2-connected spanning subgraph polyhedron has integer or half-integer extreme points. These graphs are called quasi-integer. For these graphs, the linear relaxation of the k-edge connected spanning subgraph polyhedron is integer for all k=4r, r≥1. The class of quasi-integer graphs is closed under minors and contains for instance the class of series-parallel graphs. We discuss some structural properties of graphs which are minimally non quasi-integer graphs, then we examine some basic operations which preserve the quasi-integer property. Using this, we show that the subdivisions of wheels are quasi-integer.

Keywords: k-edge connectivity; Half integrality; Polyhedron; Linear relaxation; Forbidden minors (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10878-007-9134-9

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