Geodesic
Generalized edge-chromatic numbers and additive hereditary properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 349-359

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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 hereditary properties of graphs. The generalized edge-chromatic number ρ'_() is defined as the least integer n such that ⊆ n. We investigate the generalized edge-chromatic numbers of the properties → H, ₖ, ₖ, *ₖ, ₖ and ₖ.
Keywords: property of graphs, additive, hereditary, generalized edge-chromatic number 
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Dorfling, Michael; Dorfling, Samantha. Generalized edge-chromatic numbers and additive hereditary properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 349-359. http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a10/