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Main Authors:	Irmai, Jannik, Naumann, Lucas Fabian, Andres, Bjoern
Format:	Preprint
Published:	2024
Subjects:	Discrete Mathematics Optimization and Control
Online Access:	https://arxiv.org/abs/2411.03407
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author	Irmai, Jannik Naumann, Lucas Fabian Andres, Bjoern
author_facet	Irmai, Jannik Naumann, Lucas Fabian Andres, Bjoern
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2411_03407
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Chorded cycle facets of the clique partitioning polytope Irmai, Jannik Naumann, Lucas Fabian Andres, Bjoern Discrete Mathematics Optimization and Control 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.
title	Chorded cycle facets of the clique partitioning polytope
topic	Discrete Mathematics Optimization and Control
url	https://arxiv.org/abs/2411.03407

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