Graphs with chromatic numbers strictly less than their colouring numbers

Abstract

The colouring number of a graph G, defined as col(G) = 1 + maxH⊆G ∞(H), is an upper bound for its chromatic number. In this note, we prove that it is NP-complete to determine whether an arbitrary graph G has chromatic number strictly less than its colouring number. Copyright © 2011 DMFA Slovenije.