Chromatic index of graphs of even order with many edges.

Chetwynd, Amanda G. and Hilton, A. J. W. (1984) Chromatic index of graphs of even order with many edges. Journal of Graph Theory, 8 (4). pp. 463-470. ISSN 0364-9024

Abstract

We show that, for r = 1, 2, a graph G with 2n + 2 (6) vertices and maximum degree 2n + 1 - r is of Class 2 if and only if |E(G/v)| > () - rn, where v is a vertex of G of minimum degree, and we make a conjecture for 1 r n, of which this result is a special case. For r = 1 this result is due to Plantholt.