Abstract
In a simple graphG=(X.E) a positive integerc i is associated with every nodei. We consider node colorings where nodei receives a setS(i) ofc i consecutive colors andS(i)∩S(j)=Ø whenever nodesi andj are linked inG. Upper bounds on the minimum number of colors needed are derived. The case of perfect graphs is discussed.
Zusammenfassung
In einem schlichten GraphenG=(X, E) gibt man jedem Knotenpunkti einen positiven ganzzahligen Wertc i. Wir betrachten Färbungen der Knotenpunkte, bei denen jeder Knotenpunkti eine MengeS(i) vonc i konsekutiven Farben erhält mitS(i)∩S(j)=Ø wenn die Kante [i.j] existiert. Obere Grenzen für die minimale Anzahl der Farben solcher Färbungen werden hergeleitet. Der Fall der perfekten Graphen wird auch kurz diskutiert.
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de Werra, D., Hertz, A. Consecutive colorings of graphs. Zeitschrift für Operations Research 32, 1–8 (1988). https://doi.org/10.1007/BF01920567
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DOI: https://doi.org/10.1007/BF01920567