Multipath matroids, digraph colourings, and the Tutte polynomial

Carlo Collari; Luigi Caputi; Sabino Di Trani

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Multipath matroids, digraph colourings, and the Tutte polynomial

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arxiv 2409.14528 v1 pith:IISTE4HJ submitted 2024-09-22 math.CO math.AT

Multipath matroids, digraph colourings, and the Tutte polynomial

Luigi Caputi , Carlo Collari , Sabino Di Trani This is my paper

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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.

Multipath matroids, digraph colourings, and the Tutte polynomial

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