- Tytuł:
- Generalized Sum List Colorings of Graphs
- Autorzy:
-
Kemnitz, Arnfried
Marangio, Massimiliano
Voigt, Margit - Powiązania:
- https://bibliotekanauki.pl/articles/31343297.pdf
- Data publikacji:
- 2019-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
sum list coloring
sum choice number
generalized sum list coloring
additive hereditary graph property - Opis:
- A (graph) property \( \mathcal{P} \) 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 \( \mathcal{P} \). If to each vertex $v$ of a graph $G$ a list $L(v)$ of colors is assigned, then in an \( (L, \mathcal{P} ) \)-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 \( \mathcal{P} \). The \( \mathcal{P} \)-sum choice number \( X_{sc}^\mathcal{P} (G) \) 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 \( (L, \mathcal{P} ) \)-coloring of $G$. We state some basic results on monotonicity, give upper bounds on the \( \mathcal{P} \)-sum choice number of arbitrary graphs for several properties, and determine the \( \mathcal{P} \)-sum choice number of specific classes of graphs, namely, of all complete graphs, stars, paths, cycles, and all graphs of order at most 4.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2019, 39, 3; 689-703
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł