An Elementary Integrality Proof of Rothblum's Stable Matching Formulation

TL;DR

This paper presents a concise new proof demonstrating the integrality of Rothblum's linear formulation for the convex hull of stable matchings in bipartite graphs, using an approach inspired by iterative rounding.

Contribution

It introduces a novel, simplified proof of integrality for Rothblum's stable matching formulation, enhancing theoretical understanding.

Findings

Proof confirms all extreme points are integral

Simplifies previous complex proofs

Strengthens theoretical foundation of stable matchings

Abstract

In this paper we provide a short new proof for the integrality of Rothblum's linear description of the convex hull of incidence vectors of stable matchings in bipartite graphs. In the spirit of iterative rounding proofs, the key feature of our proof is to show that extreme points of the formulation must have a 0, 1-component.