Toric rings of perfectly matchable subgraph polytopes
Kenta Mori
TL;DR
This paper investigates the algebraic properties of toric rings associated with perfectly matchable subgraph polytopes, providing a complete characterization of graphs with compressed polytopes.
Contribution
It offers a novel characterization of graphs whose perfectly matchable subgraph polytopes are compressed, advancing understanding of their algebraic structure.
Findings
Characterization of graphs with compressed polytopes
Analysis of Gorensteinness of the toric rings
Insights into algebraic properties of matchable subgraph polytopes
Abstract
The perfectly matchable subgraph polytope of a graph is a (0,1)-polytope associated with the vertex sets of matchings in the graph. In this paper, we study algebraic properties (compressedness, Gorensteinness) of the toric rings of perfectly matchable subgraph polytopes. In particular, we give a complete characterization of a graph whose perfectly matchable subgraph polytope is compressed.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics