Hypergraphs with finitely many isomorphism subtypes
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- by Henry A. Kierstead and Peter J. Nyikos PDF
- Trans. Amer. Math. Soc. 312 (1989), 699-718 Request permission
Abstract:
Let $\mathcal {H} = (H,E)$ be an $n$-uniform infinite hypergraph such that the number of isomorphism types of induced subgraphs of $\mathcal {H}$ of cardinality $\lambda$ is finite for some infinite $\lambda$. We solve a problem due independently to Jamison and Pouzet, by showing that there is a finite subset $K$ of $H$ such that the induced subgraph on $H - K$ is either empty or complete. We also characterize such hypergraphs in terms of finite (not necessarily uniform) hypergraphs.References
- James E. Baumgartner, Order types of real numbers and other uncountable orderings, Ordered sets (Banff, Alta., 1981) NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., vol. 83, Reidel, Dordrecht-Boston, Mass., 1982, pp. 239–277. MR 661296 C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973. R. Jamison, private communication. M. Pouzet, private communication.
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 312 (1989), 699-718
- MSC: Primary 05C65
- DOI: https://doi.org/10.1090/S0002-9947-1989-0988883-8
- MathSciNet review: 988883