Abstract
An s-uniform hypergraph is a hypergraph in which every edge contains exactly s vertices, while in an s+-hypergraph every edge contains at least s vertices. Let F(s) be the set of all finite sequences of non-negative integers which have a unique realisation in the set of all s-uniform hypergraphs, and let F(s+) be the corresponding set for s+-hypergraphs. Hakimi determined F(2), and F(s) can be derived from a result of Koren. Here we determine F(2+) and show that the "graph of 2+-realisations" of any sequence is connected.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Gale, A Theorem on Flows in Networks, Pacific J. Math. 7 (1957), 1073–1082.
J.E. Graver and M.E. Watkins, Combinatorics with Emphasis on the Theory of Graphs, (Springer-Verlag, New York, 1977).
S.L. Hakimi, On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph II. Uniqueness, J. Soc. Indust. Appl. Math. 11 (1963), 135–147.
M. Koren, Paris of Sequences with a Unique Realization by Bipartite Graphs, J. Combin. Theory Ser. B 21 (1976), 224–234.
H.J. Ryser, Combinatorial Properties of Matrices of Zeros and Ones, Canad. J. Math. (1957), 371–377.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Billington, D. (1980). Degree sequences uniquely realisable by hypergraphs. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088900
Download citation
DOI: https://doi.org/10.1007/BFb0088900
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10254-0
Online ISBN: 978-3-540-38376-5
eBook Packages: Springer Book Archive