On cut polytopes and graph minors

Kaparis, Konstantinos and Letchford, Adam and Mourtos, Ioannis (2023) On cut polytopes and graph minors. Discrete Optimization, 50: 100807. ISSN 1572-5286

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Abstract

The max-cut problem is a fundamental and much-studied NP-hard combinatorial optimisation problem, with a wide range of applications. Several authors have shown that the max-cut problem can be solved in polynomial time if the underlying graph is free of certain minors. We give a polyhedral counterpart of these results. In particular, we show that, if a family of valid inequalities for the cut polytope satisfies certain conditions, then there is an associated minor-closed family of graphs on which the max-cut problem can be solved efficiently.