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On cut polytopes and graph minors

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Article number100807
<mark>Journal publication date</mark>30/11/2023
<mark>Journal</mark>Discrete Optimization
Publication StatusPublished
Early online date10/10/23
<mark>Original language</mark>English


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.