2024/07/11 by Benjamin Eisley, Eisley, Benjamin, Koji Matsushita +3
Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2407.08820
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.