On a class of strong valid inequalities for the connected matching polytope

TL;DR

This paper introduces a new family of strong valid inequalities that define facets of the connected matching polytope, enhancing understanding of its structure and aiding optimization.

Contribution

It identifies a quadratic number of nontrivial facets of the connected matching polytope, providing new insights and tools for combinatorial optimization.

Findings

Identified a family of $O(|E(G)|^2)$ facets of the connected matching polytope.

Provided software tools for polytope inspection.

Enhanced the theoretical understanding of the connected matching polytope structure.

Abstract

We identify a family of $O(|E(G)|^2)$ nontrivial facets of the connected matching polytope of a graph $G$, that is, the convex hull of incidence vectors of matchings in $G$ whose covered vertices induce a connected subgraph. Accompanying software to further inspect the polytope of an input graph is available.