Perfect Matching Complexes of Polygonal Line Tilings
Abstract
The perfect matching complex of a simple graph G is a simplicial complex having facets (maximal faces) as the perfect matchings of G. This article discusses the perfect matching complex of polygonal line tilings and the (2 × n)-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 (2 × n)-grid graph that cannot be extended to form a perfect matching.
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