Graphs with chromatic numbers strictly less than their colouring numbers
Zhu, Xuding
The colouring number of a graph ▫$G$▫, defined as col▫$(G) = 1 + \max_{H\subseteq G} \delta (H)$▫, 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.
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