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arXiv · 2601.05670

Multipath complexes of bidirectional polygonal digraphs

Luigi Caputi·Carlo Collari·Jason P. Smith
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Abstract

In this work we study the homotopy type of multipath complexes of bidirectional path graphs and polygons, motivated by works of Vre\'cica and \v{Z}ivaljevi\'c on cycle-free chessboard complexes (that is, multipath complexes of complete digraphs). In particular, we show that bidirectional path graphs are homotopic to spheres and that, in analogy with cycle-free chessboard complexes, multipath complexes of bidirectional polygonal digraphs are highly connected. Using a Mayer-Vietoris spectral sequence, we provide a computation of the associated homology groups. We study T-operations on graphs, and show that this corresponds to taking suspensions of multipath complexes. We further discuss (non) shellability properties of such complexes, and present new open questions.

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Luigi Caputi, Carlo Collari, Jason P. Smith. 2026-01-09. Multipath complexes of bidirectional polygonal digraphs. https://arxiv.org/abs/2601.05670

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