The average degree of a subcubic edge-chromatic critical graph: WOODALL

A graph G is here called 3-critical if Delta(G)=3,chi '(G)=4, and chi '(G-e)=3 for every edge e of G. The 3-critical graphs include P* (the Petersen graph with a vertex deleted), and subcubic graphs that are Hajos joins of copies of P*. Building on a recent paper of Cranston and Rabern, it is proved here that if G is 3-critical and not P* nor a Hajos join of two copies of P*, then G has average degree at least 68/25=2.72; this bound is sharp, as it is the average degree of a Hajos join of three copies of P*.