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Consecutive colorings of graphs. (English) Zbl 0633.05027

In a simple graph \(G=(X,E)\) a positive integer \(c_ i\) is associated with every node i. We consider node colorings where node i receives a set S(i) of \(c_ i\) consecutive colors and \(S(i)\cap S(j)=\emptyset\) whenever nodes i and j are linked in G. Upper bounds on the minimum number of colors needed are derived. The case of perfect graphs is discussed.

MSC:

05C15 Coloring of graphs and hypergraphs
05C35 Extremal problems in graph theory
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References:

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