The average degree of an edge-chromatic critical graph

A graph G with maximum degree @D and edge chromatic number @g^'(G)>@D is [email protected] if @g^'(G-e)[email protected] for every edge e of G. New lower bounds are given for the average degree of an [email protected] graph, which improve on the best bounds previously known for most values of @D. Examples of [email protected] graphs are also given. In almost all cases, there remains a large gap between the best lower bound known and the smallest average degree of any known [email protected] graph.