Matching polytopes, Gorensteinness, and the integer decomposition property
Combinatorics
2024-07-15 v1
Abstract
The matching polytope of a graph is the convex hull of the indicator vectors of the matchings on . We characterize the graphs whose associated matching polytopes are Gorenstein, and then prove that all Gorenstein matching polytopes possess the integer decomposition property. As a special case study, we examine the matching polytopes of wheel graphs and show that they are not Gorenstein, but do possess the integer decomposition property.
Keywords
Cite
@article{arxiv.2407.08820,
title = {Matching polytopes, Gorensteinness, and the integer decomposition property},
author = {Benjamin Eisley and Koji Matsushita and Andrés R. Vindas-Meléndez},
journal= {arXiv preprint arXiv:2407.08820},
year = {2024}
}
Comments
23 pages, 11 figures, Comments welcomed!