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Realization of a sum of sequences by a sum graph

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Abstract

It is shown that the realizability of the sequences ϕ=(a 1,…, a ), ψ=(b 1,…,b n ) and ϕ+ψ is a sufficient condition for the realizability of ϕ+ψ by a graph with a ϕ-factor ifb i ≦1 fori=1,…,n. The condition is not sufficient in general. A necessary and sufficient condition for the realizability of ϕ+ψ by a graph with a ϕ-factor is given for the case that ϕ is realizable by a star and isolated vertices.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Michael Koren

  2. Department of Operations Research, Cornell University, Ithica, New York, U.S.A.

    Michael Koren

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  1. Michael Koren
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Koren, M. Realization of a sum of sequences by a sum graph. Israel J. Math. 15, 396–403 (1973). https://doi.org/10.1007/BF02757078

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  • DOI: https://doi.org/10.1007/BF02757078

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