Colorful Graph Associahedra

TL;DR

This paper introduces the colorful graph associahedron, a new combinatorial structure derived from a graph and a color palette, expanding the understanding of graph-based polytopes and their properties.

Contribution

It defines the colorful graph associahedron, proves it forms a collection of simple abstract polytopes, and explores its properties, extending classical graph associahedra.

Findings

The colorful graph associahedron is a collection of simple abstract polytopes.

The structure generalizes classical graph associahedra by incorporating colors.

Properties of the colorful graph associahedron are systematically explored.

Abstract

Given a graph G, the graph associahedron is a simple convex polytope whose face poset is based on the connected subgraphs of G. With the additional assignment of a color palette, we define the colorful graph associahedron, show it to be a collection of simple abstract polytopes, and explore its properties.