On the Δ-subgraph of graphs which are critical with respect to the chromatic index.

Chetwynd, Amanda G. and Hilton, A. J. W. and Hoffman, D. G. (1989) On the Δ-subgraph of graphs which are critical with respect to the chromatic index. Journal of Combinatorial Theory, Series B, 46 (2). pp. 240-275. ISSN 0095-8956

Abstract

The Δ-subgraph of a simple graph G is the subgraph of G induced by the vertices of maximum degree Δ = Δ(G). We show that a non-empty simple graph H can be a Δ-subgraph of a graph G, which is critical with respect to the chromatic index, if and only if H has no vertices of degree 0 or 1.