A new tool for proving Vizing’s Theorem

The known proofs of the famous theorem of Vizing on edge coloring of (multi)graphs are not long but sophisticated. The main goal of this note is to present an auxiliary (multi)digraph that simplifies and facilitates proofs of it. The secondary goal is to use the approach for proofs of Vizing’s Adjacency Lemma and the Andersen–Goldberg Theorem.