Work

Matching Polytopes, Gorensteinness, and the Integer Decomposition Property

Year: 2025

Type: article

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.

Source: Graphs and Combinatorics

DOI: 10.1007/s00373-025-02923-8

Authors: Benjamin Eisley, Koji Matsushita, Andrés R. Vindas-Meléndez

Institutions: University of California, Berkeley, The University of Osaka, Harvey Mudd College

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,190

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