On two conjectures to generalize Vizing's Theorem

Visizing's Theorem states that for a single graph G, the chromatic index q(G) is equal to the maximum degree Δ(G) or to Δ(G)+1. To extend this theorem to some classes of hypergraphs, we suggest two conjectures, non-comparable, but, in some sense, dual, which are discussed in the present paper.