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The Minimal Integral Separator of A Threshold Graph

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DOI: 10.1016/s0167-5060(08)70749-0
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  • Computer Science

Abstract

A graph is called threshold if there exists a real number b and real numbers a j associated with its vertices w j such that Σ a j ≤ b holds iff S is a stable (independent) set of vertices. The vector 〈 a 1,…, a n; b〉 associated to a threshold graph is called an integral separator if a i + a j ≥ b + 1 for every edge ( w i w j ). A simple algorithm is presented to determine for a given threshold graph its (unique) integral separator which minimizes b.

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