Compositions in the bipartite subgraph polytope

The perfectly matchable subgraph polytope

The following type of problem arises in practice: in a node-weighted graph G, find a minimum weight node set that satisfies certain conditions and, in addition, induces a perfectly matchable subgraph of G. This has led us to study the convex hull of incidence vectors of node sets that induce perfectly matchable subgraphs of a graph G, which we call the perfectly matchable subgraph polytope of G...

Testing the Odd Bicycle Wheel Inequalities for the Bipartite Subgraph Polytope

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Small bipartite subgraph polytopes

We compute a complete linear description of the bipartite subgraph polytope, for up to seven nodes, and a conjectured complete description for eight nodes. We then show how these descriptions were used to compute the integrality ratio of various relaxations of the max-cut problem, again for up to eight nodes.

New facets for the planar subgraph polytope

This paper describes certain facet classes for the planar subgraph polytope. These facets are extensions of Kuratowski facets and are of the form 2x(U)+x(E(G)\U) ≤ 2|U |+|E(G)\U | −2 where the edge set U varies and can be empty. Two of the new types of facets complete the class of extended subdivision facets, explored by Jünger and Mutzel. In addition, the other types of facets consist of a new...

On the Facial Structure of the Common Edge Subgraph polytope