Matching trees for simplicial complexes and homotopy type of devoid complexes of graphs

TL;DR

This paper extends homotopy computation methods like splittings and matching trees from independence complexes to general simplicial complexes, demonstrating their effectiveness on devoid complexes and computing the homotopy type of dominance complexes in chordal graphs.

Contribution

It introduces generalized homotopy calculation techniques for simplicial complexes and applies them to specific complexes related to graphs, such as devoid and dominance complexes.

Findings

Efficient homotopy calculations for devoid complexes of graphs

Homotopy type determination of dominance complexes in chordal graphs

Generalization of matching tree techniques to arbitrary simplicial complexes

Abstract

We generalize some homotopy calculation techniques such as splittings and matching trees that are introduced for the computations in the case of the independence complexes of graphs to arbitrary simplicial complexes, and exemplify their efficiency on some simplicial complexes, the devoid complexes of graphs, which are simplicial complexes parametrized by graphs. Additionally, we compute the homotopy type of dominance complexes of chordal graphs.