Abstract
A sequence {d 1, d 2, . . . , d n } of nonnegative integers is graphic (multigraphic) if there exists a simple graph (multigraph) with vertices v 1, v 2, . . . , v n such that the degree d(v i ) of the vertex v i equals d i for each i = 1, 2, . . . , n. The (multi) graphic degree sequence problem is: Given a sequence of nonnegative integers, determine whether it is (multi)graphic or not. In this paper we characterize sequences that are multigraphic in a similar way, Havel (Časopis Pěst Mat 80:477–480, 1955) and Hakimi (J Soc Indust Appl Math 10:496–506, 1962) characterized graphic sequences. Results of Hakimi (J Soc Indust Appl Math 10:496–506, 1962) and Butler, Boesch and Harary (IEEE Trans Circuits Syst CAS-23(12):778–782, 1976) follow.
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References
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Meierling, D., Volkmann, L. A remark on degree sequences of multigraphs. Math Meth Oper Res 69, 369–374 (2009). https://doi.org/10.1007/s00186-008-0265-2
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DOI: https://doi.org/10.1007/s00186-008-0265-2