Generalized Sum List Colorings of Graphs

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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 v of a graph G a list L(v) of colors is assigned, then in an (L, 𝒫)-coloring of G every vertex obtains a color from its list and the subgraphs of G induced by vertices of the same color are always in 𝒫. The 𝒫-sum choice number Xsc𝒫(G) of G is the minimum of the sum of all list sizes such that, for any assignment L of lists of colors with the given sizes, there is always an (L, 𝒫)-coloring of G.

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.

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Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information


IMPACT FACTOR 2017: 0.601
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CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.763
Source Normalized Impact per Paper (SNIP) 2018: 0.934

Mathematical Citation Quotient (MCQ) 2017: 0.36

Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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