Geodesic
Graphs with chromatic numbers strictly less than their colouring numbers
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 25-27.

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The colouring number of a graph G, defined as col(G) = 1+ maxH ⊆ G δ(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.
DOI : 10.26493/1855-3974.176.704
Keywords: Chromatic number, colouring number, Szekeres-Wilf inequality, NP-completeness 
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Xuding Zhu. Graphs with chromatic numbers strictly less than their colouring numbers. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 25-27. doi : 10.26493/1855-3974.176.704. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.176.704/

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