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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Better-Quasi-Ordering
Countable Series-Parallel Orders


Author: Stéphan Thomassé
Journal: Trans. Amer. Math. Soc. 352 (2000), 2491-2505
MSC (1991): Primary 05C20; Secondary 05C05, 08A65, 05C75
Published electronically: April 7, 1999
MathSciNet review: 1624214
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Abstract: We prove that any infinite sequence of countable series-parallel orders contains an increasing (with respect to embedding) infinite subsequence. This result generalizes Laver's and Corominas' theorems concerning better-quasi-order of the classes of countable chains and trees.


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Additional Information

Stéphan Thomassé
Affiliation: Laboratoire LMD, UFR de Mathématiques, Université Claude Bernard 43, Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
Email: thomasse@jonas.univ-lyon1.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02400-9
PII: S 0002-9947(99)02400-9
Keywords: Better-quasi-order, interval, series-parallel graphs, series-parallel orders, structured trees, well-quasi-order
Received by editor(s): October 4, 1995
Received by editor(s) in revised form: January 6, 1998
Published electronically: April 7, 1999
Additional Notes: This work was supported in part by the DIMANET program, Human Capital and Mobility (HCM) Contract No. ERBCHRXCT 940429
Article copyright: © Copyright 2000 American Mathematical Society