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Hypergraphs With Finitely Many Isomorphism Subtypes

Henry A. Kierstead and Peter J. Nyikos
Transactions of the American Mathematical Society
Vol. 312, No. 2 (Apr., 1989), pp. 699-718
DOI: 10.2307/2001007
Stable URL: http://www.jstor.org/stable/2001007
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hypergraphs With Finitely Many Isomorphism Subtypes
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Abstract

Let $\mathscr{H} = (H, E)$ be an $n$-uniform infinite hypergraph such that the number of isomorphism types of induced subgraphs of $\mathscr{H}$ 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.

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