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Tournaments and Orders with the Pigeonhole Property

Published online by Cambridge University Press:  20 November 2018

Anthony Bonato ,
Peter Cameron  and
Dejan Delić
Anthony Bonato
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, email: abonato@wlu.ca
Peter Cameron
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, London E1 4NS, U.K., email: P.J.Cameron@qmw.ac.uk
Dejan Delić
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, email: delicd@math.mcmaster.ca
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Abstract

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A binary structure $S$ has the pigeonhole property $\left( P \right)$ if every finite partition of $S$ induces a block isomorphic to $S$. We classify all countable tournaments with $\left( P \right)$; the class of orders with $\left( P \right)$ is completely classified.

Keywords

05C2003C15pigeonhole propertytournamentorder
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 4 , 01 December 2000 , pp. 397 - 405
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Bonato, A. and Delić, D., A pigeonhole principle for relational structures. Mathematical Logic Quarterly 45 (1999), 409–413.Google Scholar
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[3] Cameron, P. J., The random graph. In: Algorithms and Combinatorics, Springer Verlag, New York 14 (1997), 333–351.Google Scholar
[4] Rosenstein, J. G., Linear orderings, Academic Press, New York, 1982.Google Scholar