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math.CO2026
Multipath complexes of bidirectional polygonal digraphs
Luigi Caputi, Carlo Collari, Jason P. Smith
In this work we study the homotopy type of multipath complexes of bidirectional path graphs and polygons, motivated by works of Vrećica and Živaljević on cycle-free chessboard comp…
math.CO2024
Multipath matroids, digraph colourings, and the Tutte polynomial
Luigi Caputi, Carlo Collari, Sabino Di Trani
We characterise the digraphs for which the multipaths, that is disjoint unions of directed paths, yield a matroid. For such graphs, called MP-digraphs, we prove that the Tutte poly…