Matching Polytopes, Gorensteinness, and the Integer Decomposition Property
Abstract The matching polytope of a graph G is the convex hull of the indicator vectors of the matchings on G . 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.
Authors
- Koji Matsushita (ORCID: https://orcid.org/0009-0008-6147-6711)
- Andrés R. Vindas-Meléndez (ORCID: https://orcid.org/0000-0002-7437-3745)
- Benjamin Eisley
Institutions
- Harvey Mudd College (US)
- University of California, Berkeley (US)
- The University of Osaka (JP)
Publication Details
- Journal
- Graphs and Combinatorics
- Published
- 2025-04-16
- DOI
- https://doi.org/10.1007/s00373-025-02923-8
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Japan Society for the Promotion of Science London
- Directorate for Mathematical and Physical Sciences
- Japan Society for the Promotion of Science