The independence number of an edge-chromatic critical graph
A graph G with maximum degree ? and edge chromatic number ??(G)>? is edge-?-critical if ??(G?e)=? for every edge e of G. It is proved here that the vertex independence number of an edge-?-critical graph of order n is less than . For large ?, this improves on the best bound previously known, which was roughly ; the bound conjectured by Vizing, which would be best possible, is .  2010 Wiley Periodicals, Inc. J Graph Theory 66:98-103, 2011
adjacency lemma chromatic index edge coloring edge-critical graph