Minimum order of graphs with given coloring parameters
نویسندگان
چکیده
A complete k-coloring of a graph G = (V,E) is an assignment φ : V → {1, . . . , k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively), and the Grundy number Γ(G) defined as the largest k admitting a complete coloring φ with exactly Research partially supported by National Science Centre under contract DEC2011/02/A/ST6/00201 † Research supported in part by the Hungarian Scientific Research Fund, OTKA grant no. 81493, and by the Hungarian State and the European Union under the grant TAMOP-4.2.2.A-11/1/ KONV2012-0072.
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عنوان ژورنال:
- Discrete Mathematics
دوره 338 شماره
صفحات -
تاریخ انتشار 2015