SOME CONSEQUENCES OF A THEOREM ON FANS

Abstract

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 $\chi'(G) \gt \Delta(G)$) 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].