Independence complexes of hypergraphs and bounded degree complexes

TL;DR

This paper proves that bounded degree complexes of forests are shellable by analyzing independence complexes of hypergraphs, and provides a wedge decomposition for these complexes when the graph has a leaf.

Contribution

It introduces a new approach to study bounded degree complexes using hypergraph independence complexes and establishes shellability for forests.

Findings

Bounded degree complexes of forests are shellable.

A wedge decomposition for bounded degree complexes is obtained when the graph has a leaf.

The approach connects hypergraph independence complexes with topological properties of bounded degree complexes.

Abstract

The bounded degree complex $BD(G,\lambda)$ is a generalization of the matching complexes of a graph. In this paper, we show that the bounded degree complex of a forest is shellable, by using independence complexes of hypergraphs. We obtain a wedge decomposition result of bounded degree complexes when a graph $G$ has a leaf