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Chromatic scheduling and frequency assignment. (English) Zbl 0801.90067

Summary: Some extensions of classical coloring models are developed; these consist in assigning to each node a set of consecutive colors; furthermore for each oriented arc \((i,j)\) in a graph a set \(T_{ij}\) of consecutive integers is given. It is required to find an assignment of colors to the nodes such that for each arc \((i,j)\) the first colors \(f(i)\), \(f(j)\) given to nodes \(i\) and \(j\) satisfying \(f(j)- f(i)\not\in T_{ij}\). This model can be used for assigning frequencies to a collection of stations as well as for chromatic scheduling problems. Simple upper bounds on the generalized chromatic number are derived. Computational results are reported for some randomly generated problems.

MSC:

90B35 Deterministic scheduling theory in operations research
05C15 Coloring of graphs and hypergraphs
90B30 Production models
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References:

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