Decomposable edge polytopes of finite graphs

TL;DR

This paper investigates the structure of decomposable edge polytopes derived from finite graphs, clarifying the relationship between different types of decomposability and providing a characterization of such graphs.

Contribution

It offers a detailed analysis of graphs with decomposable edge polytopes, addressing key questions about their classification and properties, extending prior algebraic-focused research.

Findings

Characterization of decomposable graphs

Relationship between type I and type II decompositions

Criteria for graph decomposability

Abstract

Edge polytopes is a class of interesting polytope with rich algebraic and combinatorial properties, which was introduced by Ohsugi and Hibi. In this papar, we follow a previous study on cutting edge polytopes by Hibi, Li and Zhang. Instead of focusing on the algeraic properties of the subpolytopes as the previous study, in this paper, we take a closer look on the graphs whose edge polytopes are decomposable. In particular, we answer two important questions raised in the previous study about 1) the relationship between type I and type II decomposable graphs and 2) description of decomposable graphs.