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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Degree sequences in complexes and hypergraphs


Author: A. K. Dewdney
Journal: Proc. Amer. Math. Soc. 53 (1975), 535-540
MSC: Primary 05C99; Secondary 55A15
MathSciNet review: 0384610
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Abstract: Given an $ n$-complex $ K$ and a vertex $ v$ in $ K$, the $ n$-degree of $ v$ is the number of $ n$-simplexes in $ K$ containing $ v$. The set of all $ n$-degrees in a complex $ K$ is called its $ n$-degree sequence when arranged in nonincreasing order. The question ``Which sequences of integers are $ n$-degree sequences?'' is answered in this paper. This is done by generalizing the iterative characterization for the $ 1$-dimensional (graphical) case due to V. Havel. A corollary to this general theorem yields the analogous generalization for $ k$-graphs. The characterization of P. Erdös and T. Gallai is discussed briefly.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0384610-1
PII: S 0002-9939(1975)0384610-1
Article copyright: © Copyright 1975 American Mathematical Society