Connectivity and Whitney inequalities for directed hypergraphs

Directed hypergraphs give rise to many different notions of connectedness, in this talk I will briefly talk of some notions, focusing on the connectivity definition based on the simplest, least restrictive, construction of hyperpaths. Besides that, I will talk about a generalized version of Whitney's inequalities, which relates vertex connectivity under strong removal, hyperedge connectivity under weak removal, and a degree parameter analogous to those defined in the Whitney inequalities for digraphs. Finally, I will speak of the relation between the connectivity indices of the directed hypergraphs with those of their bipartite representation or König representation.