On the homotopy type of multipath complexes

Caputi, L, Collari, C, Di Trani, S and Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604, 2024. On the homotopy type of multipath complexes. Mathematika, 70 (1): e12235. ISSN 0025-5793

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Abstract

A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph G is the simplicial complex whose faces are the multipaths of G. We compute Euler characteristics, and associated generating functions, of the multipath complexes of directed graphs from certain families, including transitive tournaments and complete bipartite graphs. We show that if G is a linear graph, polygon, small grid or transitive tournament, then the homotopy type of the multipath complex of G is always contractible or a wedge of spheres. We introduce a new technique for decomposing directed graphs into dynamical regions, which allows us to simplify the homotopy computations.

Item Type:	Journal article
Publication Title:	Mathematika
Creators:	Caputi, L., Collari, C., Di Trani, S. and Smith, J.P.
Publisher:	Wiley
Date:	January 2024
Volume:	70
Number:	1
ISSN:	0025-5793
Identifiers:	Number Type 10.1112/mtk.12235 DOI 1844094 Other
Rights:	© 2023 The Authors. The publishing rights in this article are licensed to University College London under an exclusive licence. Mathematika is published by the London Mathematical Society on behalf of University College London. This is the pre-peer reviewed version of the following article: Caputi, L., Collari, C., Di Trani, S., & Smith, J. P. (2024). On the homotopy type of multipath complexes. Mathematika, 70(1), Article e12235. , which has been published in final form at https://doi.org/10.1112/mtk.12235. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Divisions:	Schools > School of Science and Technology
Record created by:	Linda Sullivan
Date Added:	12 Dec 2023 12:13
Last Modified:	12 Dec 2023 12:13
URI:	https://irep.ntu.ac.uk/id/eprint/50523

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