Geodesic
Generalized chromatic numbers and additive hereditary properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 259-270

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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let and be additive hereditary properties of graphs. The generalized chromatic number χ_() is defined as follows: χ_() = n iff ⊆ ⁿ but ⊊ ^n-1. We investigate the generalized chromatic numbers of the well-known properties of graphs ₖ, ₖ, ₖ, ₖ and ₖ.
Keywords: property of graphs, additive, hereditary, generalized chromatic number 
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Broere, Izak; Dorfling, Samantha; Jonck, Elizabeth. Generalized chromatic numbers and additive hereditary properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 259-270. http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a4/