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arXiv · 2411.03407

Chorded cycle facets of the clique partitioning polytope

Jannik Irmai·Lucas Fabian Naumann·Bjoern Andres
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Abstract

The $q$-chorded $k$-cycle inequalities are a class of valid inequalities for the clique partitioning polytope. It is known that for $q \in \{2, \tfrac{k-1}{2}\}$, these inequalities induce facets of the clique partitioning polytope if and only if $k$ is odd. Here, we characterize such facets for arbitrary $k$ and $q$. More specifically, we prove that the $q$-chorded $k$-cycle inequalities induce facets of the clique partitioning polytope if and only if two conditions are satisfied: $k = 1$ mod $q$, and if $k=3q+1$ then $q=3$ or $q$ is even. This establishes the existence of many facets induced by $q$-chorded $k$-cycle inequalities beyond those previously known.

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Jannik Irmai, Lucas Fabian Naumann, Bjoern Andres. 2024-11-05. Chorded cycle facets of the clique partitioning polytope. https://arxiv.org/abs/2411.03407

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