Überblick

Open Access

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Peer Reviewed

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Abstract

• A (graph) property 𝒫 is a class of simple finite graphs closed under isomorphisms. In this paper we consider generalizations of sum list colorings of graphs with respect to properties 𝒫. If to each vertex of a graph a list ) of colors is assigned, then in an ( 𝒫)-coloring of every vertex obtains a color from its list and the subgraphs of induced by vertices of the same color are always in 𝒫. The 𝒫-sum choice number of is the minimum of the sum of all list sizes such that, for any assignment of lists of colors with the given sizes, there is always an ( 𝒫)-coloring of We state some basic results on monotonicity, give upper bounds on the 𝒫-sum choice number of arbitrary graphs for several properties, and determine the 𝒫-sum choice number of specific classes of graphs, namely, of all complete graphs, stars, paths, cycles, and all graphs of order at most 4.

authors

• Arnfried Kemnitz
• Marangio, Massimiliano
• Margit Voigt

Veröffentlichungszeitpunkt

• Januar 8, 2019

veröffentlicht in

• Discussiones Mathematicae. Graph Theory, Vol.39(3), pp. 689-703  Zeitschrift