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

 

Normal tree orders for infinite graphs


Authors: J.-M. Brochet and R. Diestel
Journal: Trans. Amer. Math. Soc. 345 (1994), 871-895
MSC: Primary 05C05
MathSciNet review: 1260198
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Abstract: A well-founded tree T denned on the vertex set of a graph G is called normal if the endvertices of any edge of G are comparable in T. We study how normal trees can be used to describe the structure of infinite graphs. In particular, we extend Jung's classical existence theorem for trees of height $ \omega $ to trees of arbitrary height. Applications include a structure theorem for graphs without large complete topological minors. A number of open problems are suggested.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1260198-4
PII: S 0002-9947(1994)1260198-4
Article copyright: © Copyright 1994 American Mathematical Society