Integral Polyhedra Related to Even Cycle and Even Cut Matroids

  • Authors:

  • Bertrand Guenin

  • Affiliations:

  • -

  • Venue:
  • Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
  • Year:
  • 2001

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Abstract

A family of sets H is ideal if the polyhedron {x ≥ 0 : Σi∈S xi ≥ 1; ∀S ∈ H} is integral. Consider a graph G with vertices s, t. An odd st-walk is either: an odd st-path; or the union of an even st-path and an odd circuit which share at most one vertex. Let T be a subset of vertices of even cardinality. An st-T-cut is a cut of the form σ(U) where |U ∩ T| is odd and U contains exactly one of s or t. We give excluded minor characterizations for when the families of odd st-walks and st-T-cuts (represented as sets of edges) are ideal. As a corollary we characterize which extensions and coextensions of graphic and cographic matroids are 1-flowing.