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 class of facets for the polytope called 3-star subdivisions. It is also shown that the extended and 3-star subdivision facets are also equivalent to members of the class of facets with coefficients in {0,1,2} for the set covering polytope. Computational results displaying the effectiveness of the facets in a branch-and-cut scheme for the maximum planar subgraph problem are presented. keywords: planar graph, planar subgraph polytope, polyhedral combinatorics