SOME CONSEQUENCES OF A THEOREM ON FANS

Using a fundamental identity concerning fans called "Fan Theorem" we give new proofs of classical edge colouring theorems. We also derive from the same identity a formula for the chromatic index of Class 2 multigraphs (i.e. multigraphs G such that χ′(G) > Δ(G)) and a new generalization of Vizing's Adjacency Lemma to multigraphs, which is more general than the one given by the author in [D. Cariolaro, On fans in multigraphs, J. Graph Theory, 51 (4), 2006, 301-318].