Abstract:For a simple graph G, denote by n, ∆(G), and χ (G) its order, maximum degree, and chromatic index, respectively. A connected class 2 graph G is edge-chromatic critical if χ (G − e) < ∆(G) + 1 for every edge e of G. Define G to be overfull if |E(G)| > ∆(G) n/2 . Clearly, overfull graphs are class 2 and any graph obtained from a regular graph of even order by splitting a vertex is overfull. Let G be an nvertex connected regular class 1 graph with ∆(G) > n/3. Hilton and Zhao in 1997 conjectured that if G * is obt… Show more
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