Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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L. Caputi - C. Collari - S. Di Trani - J. P. Smith

On the homotopy type of multipath complexes

created by collari on 10 Aug 2022
modified on 25 Sep 2024

[BibTeX]

Published Paper

Inserted: 10 aug 2022
Last Updated: 25 sep 2024

Journal: Mathematika
Volume: 70
Number: 1
Year: 2022
Doi: 10.1112/mtk.12235

ArXiv: 2208.04656 PDF

Abstract:

A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph ${\tt G}$ is the simplicial complex whose faces are the multipaths of ${\tt G}$. We compute the Euler characteristic, and associated generating function, of the multipath complex for some families of graphs, including transitive tournaments and complete bipartite graphs. Then, we compute the homotopy type of multipath complexes of linear graphs, polygons, small grids and transitive tournaments. We show that they are all contractible or wedges of spheres. We introduce a new technique for decomposing directed graphs into dynamical regions, which allows us to simplify the homotopy computations.

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