A Δ-subgraph condition for a graph to be class 1.

Chetwynd, Amanda G. and Hilton, A. J. W. (1989) A Δ-subgraph condition for a graph to be class 1. Journal of Combinatorial Theory, Series B, 46 (1). pp. 37-45. ISSN 0095-8956

Abstract

The Δ-subgraph GΔ of a simple graph G is the subgraph of G induced by the vertices of maximum degree Δ = Δ(G). We prove a number of results to the effect that if Δ(G) is large and the minimum degree of GΔ is at most one, then G satisfies χ′(G) = Δ(G), where χ′(G) is the edge-chromatic number of G.