Shellable posets arising from the even subgraphs of a graph

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Abstract

The concept of a poset of even subgraphs of a graph was firstly considered by S. Choi and H. Park to compute the rational Betti numbers of a real toric manifold associated with a simple graph. 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.

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