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arXiv · 2311.06017

Extended formulations for the integer hull of strictly $\Delta$-modular cographic polyhedral cones

Joseph Paat·Zach Walsh·Luze Xu
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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 $\Delta$-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.

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Joseph Paat, Zach Walsh, Luze Xu. 2023-11-10. Extended formulations for the integer hull of strictly $\Delta$-modular cographic polyhedral cones. https://arxiv.org/abs/2311.06017

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