6 citations · 28 across the 20 of their papers we have counts for
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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…
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…
On the homotopy type of multipath complexes
Luigi Caputi, Carlo Collari, Sabino Di Trani +1
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph is the simplicial complex whose faces are the multipaths of ${\tt…
Monotone cohomologies and oriented matchings
Luigi Caputi, Daniele Celoria, Carlo Collari
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs,…
Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology
Luigi Caputi, Carlo Collari, Sabino Di Trani
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path pos…