Multipath matroids, digraph colourings, and the Tutte polynomial
Combinatorics
2024-09-24 v1 Algebraic Topology
Abstract
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 polynomial of the multipath matroid is related to counting certain digraph colourings. Finally, we prove that, for MP-forests, the decategorification of the multipath cohomology yields a specialisation of the Tutte polynomial.
Keywords
Cite
@article{arxiv.2409.14528,
title = {Multipath matroids, digraph colourings, and the Tutte polynomial},
author = {Luigi Caputi and Carlo Collari and Sabino Di Trani},
journal= {arXiv preprint arXiv:2409.14528},
year = {2024}
}
Comments
23 pages, 15 figures, comments are welcome