The edge chromatic class of graphs with maximum degree at least $|V| - 3$.

Chetwynd, Amanda G. and Hilton, A. J. W. (1988) The edge chromatic class of graphs with maximum degree at least $|V| - 3$. Annals of Discrete Mathematics, 41 (C). pp. 91-110. ISSN 0167-5060

Abstract

We characterize the simple graphs G which satisfy Δ(G) ≥ |V(G)| – 3 and x'(G) = Δ(G), where x'(G) is the chromatic index of G and Δ(G) is the maximum degree of G.