The average degree of an edge-chromatic critical graph Original Research Article

A graph G with maximum degree image and edge chromatic number image is edge-image-critical if image for every edge e of G. New lower bounds are given for the average degree of an edge-image-critical graph, which improve on the best bounds previously known for most values of image. Examples of edge-image-critical 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 edge-image-critical graph.