Boolean quadric polytopes are faces of linear ordering polytopes

TL;DR

This paper demonstrates that boolean quadric polytopes are linearly isomorphic to faces of linear ordering polytopes, revealing a structural relationship between these two important classes of polytopes.

Contribution

It establishes that boolean quadric polytopes can be represented as faces of linear ordering polytopes, providing new insights into their geometric structure.

Findings

Boolean quadric polytopes are faces of linear ordering polytopes.

BQP(n) is linearly isomorphic to a face of LOP(2n).

Structural relationship between BQP and LOP polytopes.

Abstract

Let $BQP(n)$ be a boolean quadric polytope, $LOP(m)$ be a linear ordering polytope. It is shown that $BQP(n)$ is linearly isomorphic to a face of $LOP(2n)$.