Matching complexes of small grids

Abstract

The matching complex $M(G)$ of a simple graph $G$ is the simplicial complex consisting of the matchings on $G$. The matching complex $M(G)$ is isomorphic to the independence complex of the line graph $L(G)$. Braun and Hough introduced a family of graphs ${\Delta }_n^m$, which is a generalization of the line graph of the $(n\times 2)$-grid graph. In this paper, we show that the independence complex of ${\Delta }_n^m$ is a wedge of spheres. This gives an answer to a problem suggested by Braun and Hough.

arXiv comment7 pages, 6 figures, to appear in the Electronic Journal of Combinatorics

Cited by in corpus (1)

• Matching complexes of polygonal line tilings