Bounds on the size of critical edge-chromatic graphs

By Vizing's theorem, the chromatic index chi'(G) of a simple graph G satisfies Delta(G) less than or equal to chi'(G) less than or equal to Delta(G) + 1; if chi'(G) = Delta(G), then G is class 1, otherwise G is class 2. A graph G is called critical edge-chromatic graph if G is connected, class 2 and chi'(H) < chi'(G) for all proper subgraphs H of G. We give new lower bounds for the size of Delta-critical edge-chromatic graphs, for Delta greater than or equal to 9.