Multipath matroids, digraph colourings, and the Tutte polynomial
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916406203777024 |
|---|---|
| author | Caputi, Luigi Collari, Carlo Di Trani, Sabino |
| author_facet | Caputi, Luigi Collari, Carlo Di Trani, Sabino |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multipath matroids, digraph colourings, and the Tutte polynomial Caputi, Luigi Collari, Carlo Di Trani, Sabino Combinatorics Algebraic Topology 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. |
| title | Multipath matroids, digraph colourings, and the Tutte polynomial |
| topic | Combinatorics Algebraic Topology |
| url | https://arxiv.org/abs/2409.14528 |