Matching complexes of polygonal line tilings

TL;DR

This paper determines the homotopy types and connectivities of matching complexes for polygonal line tilings, advancing understanding of their topological structure.

Contribution

It provides a recursive method to explicitly determine the homotopy types and connectivities of these matching complexes, building on prior lower bounds.

Findings

Homotopy types of matching complexes are explicitly determined.

Connectivities of these complexes are precisely calculated.

Recursive formulas are established for their topological classification.

Abstract

The matching complex of a simple graph $G$ is a simplicial complex consisting of the matchings on $G$. Jeli\'c Milutinovi\'c et al. studied the matching complexes of the polygonal line tilings, and they gave a lower bound for the connectivity of the matching complexes of polygonal line tilings. In this paper, we determine the homotopy types of the matching complexes of polygonal line tilings recursively, and determine their connectivities.