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arXiv · 1606.05811

Every rational polyhedron has finite split rank: new proof

Kanstantsin Pashkovich
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Abstract

Split rank of a rational polyhedron is finite. The well known proof of this is based on the fact that split closure is stronger than the Chv\'{a}tal closure, and the Chv\'{a}tal rank of a rational polyhedron is finite due to the result of Chv\'{a}tal and Schrijver. In this note we provide an independent proof for the fact that every rational polyhedron has finite split rank. In principal, we construct a nonnegative potential function which decreases by at least one with "every" second split closure unless the integer hull of the polyhedron is reached.

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Kanstantsin Pashkovich. 2016-06-18. Every rational polyhedron has finite split rank: new proof. https://arxiv.org/abs/1606.05811

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