Extended formulations for the integer hull of strictly Δ-modular cographic polyhedral cones

Abstract

Conforti et al. give a compact extended formulation for a class of bimodular-constrained integer programs, namely those that model the stable set polytope of a graph with no disjoint odd cycles. We extend their techniques to design compact extended formulations for the integer hull of translated polyhedral cones whose constraint matrix is strictly Δ-modular and has rows that represent a cographic matroid. Our work generalizes the important special case from Conforti et al. concerning 4-connected graphs with odd cycle transversal number at least 4. We also discuss the necessity of our assumptions.