Pseudograph associahedra

TL;DR

This paper extends the concept of graph associahedra to pseudographs with loops and multiple edges, exploring their construction and how they deform under graph modifications.

Contribution

It introduces a general framework for pseudograph associahedra and analyzes their behavior under edge contractions and deletions.

Findings

Defined pseudograph associahedra including loops and multiple edges

Constructed these polytopes in a broad, generalized setting

Studied deformations of pseudograph associahedra under graph modifications

Abstract

Given a simple graph G, the graph associahedron KG is a simple polytope whose face poset is based on the connected subgraphs of G. This paper defines and constructs graph associahedra in a general context, for pseudographs with loops and multiple edges, which are also allowed to be disconnected. We then consider deformations of pseudograph associahedra as their underlying graphs are altered by edge contractions and edge deletions.