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Multicoloring the incidentors of a weighted directed multigraph

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Abstract

Under study are the directed multigraphs with weighted arcs. In multicoloring incidentors, each incidentor is endowed with a multicolor, i.e., an interval of colors whose length is equal to the weight of the incidentor. A multicoloring is admissible if the multicolors of adjacent incidentors are disjoint and, for every arc, the left endpoint of its initial incidentor is at most the left endpoint of the multicolor of its final incidentor. The lower and upper bounds are presented for the minimal number of colors necessary for an admissible multicoloring of all incidentors of a multigraph.

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References

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    V. G. Vizing

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  1. V. G. Vizing
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Correspondence to V. G. Vizing.

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Original Russian Text © V.G. Vizing, 2014, published in Diskretnyi Analiz i Issledovanie Operatsii, 2014, Vol. 21, No. 4, pp. 33–41.

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Vizing, V.G. Multicoloring the incidentors of a weighted directed multigraph. J. Appl. Ind. Math. 8, 604–608 (2014). https://doi.org/10.1134/S1990478914040188

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  • DOI: https://doi.org/10.1134/S1990478914040188

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