Bounds on the connectivity of the independence complexes of hypergraphs

TL;DR

This paper establishes lower bounds on the connectivity of independence complexes in hypergraphs and determines their homotopy types for specific classes, advancing understanding of their topological properties.

Contribution

It introduces new lower bounds for hypergraph independence complexes and characterizes their homotopy types for certain hypergraph classes.

Findings

Lower bounds on connectivity of independence complexes

Homotopy types of independence complexes for d-uniform hypergraphs

Results applicable to properly-connected triangulated hypergraphs

Abstract

We provide lower bounds on the connectivity of the independence complexes of hypergraphs. Additionally, we compute the homotopy types of the independence complexes of $d$-uniform properly-connected triangulated hypergraphs.