Multipath matroids, digraph colourings, and the Tutte polynomial

We introduce the MP-digraphs, a class of directed graphs for which the multipaths yield a matroid. We show that the family of MP-digraphs is closed under deletion and MP-contraction. We relate an evaluation of the Tutte polynomial of multipath matroids to certain digraph colourings. Finally, for MP-graphs whose underlying graph is a forest, we prove that the decategorification of multipath cohomology gives a specialisation of the Tutte polynomial – further linking path poset properties with combinatorial invariants of digraphs.