English

Matching polytopes, Gorensteinness, and the integer decomposition property

Combinatorics 2024-07-15 v1

Abstract

The matching polytope of a graph GG is the convex hull of the indicator vectors of the matchings on GG. 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!

R2 v1 2026-06-28T17:37:54.274Z