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A (general) polygonal line tiling is a graph formed by a string of cycles,each intersecting the previous at an edge, no three intersecting. In 2022,Matsushita proved the matching complex of a certain type of polygonal linetiling with even cycles is homotopy equivalent to a wedge of spheres. In thispaper, we extend Matsushita's work to include a larger family of graphs andcarry out a closer analysis of lines of triangle and pentagons, where theFibonacci numbers arise.

General polygonal line tilings and their matching complexes