On shellability for a poset of even subgraphs of a graph

TL;DR

This paper characterizes graphs with multiple edges whose posets of even subgraphs are shellable, and computes Betti numbers of associated real toric manifolds, advancing topological understanding of these structures.

Contribution

It provides a complete characterization of graphs with multiple edges that have shellable posets of even subgraphs, extending previous work to more general graphs.

Findings

Characterization of graphs with shellable posets of even subgraphs

Computation of Betti numbers for specific real toric manifolds

Extension of shellability results to graphs with multiple edges

Abstract

Given a simple graph $G$, a poset of its even subgraphs was firstly considered by S. Choi and H. Park to study the topology of a real toric manifold associated with $G$. S. Choi and the authors extended this to a graph allowing multiple edges, motivated by the work on the pseudograph associahedron of Carr, Devadoss and Forcey. In this paper, we completely characterize the graphs (allowing multiple edges) whose posets of even subgraphs are always shellable. By the result, we also compute the Betti numbers of a real toric manifold corresponding to a path with two multiple edges.