Perfect Matching Complexes of Polygonal Line Tilings
Abstract
The perfect matching complex of a simple graph is a simplicial complex having facets (maximal faces) as the perfect matchings of . This article discusses the perfect matching complex of polygonal line tilings and the -grid graph in particular. We use tools from discrete Morse theory to show that the perfect matching complex of any polygonal line tiling is either contractible or homotopy equivalent to a wedge of spheres. While proving our results, we also characterize all the matchings of -grid graph that cannot be extended to form a perfect matching.
Keywords
Cite
@article{arxiv.2407.05809,
title = {Perfect Matching Complexes of Polygonal Line Tilings},
author = {Himanshu Chandrakar and Anurag Singh},
journal= {arXiv preprint arXiv:2407.05809},
year = {2025}
}
Comments
The original element-pairing proof of Theorem 3.3, replaced in the accepted version by a shorter argument using the fold lemma (suggested by the referee), is now included in the appendix. The proof of Lemma 3.1 has been rephrased for clarity, though the reasoning remains unchanged. Published in Annals of Combinatorics (05 April 2025)