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On the reconstruction of locally finite trees

✍ Scribed by Thomas Andreae

Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
676 KB
Volume
5
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

We prove a theorem saying, when taken together with previous results of Bondy, Hemminger, and Thomassen, that every locally finite, infinite tree not containing a subdivision of the dyadic tree (i. e., the regular tree of degree 3) is uniquely determined, up to isomorphism, from its collection of vertex‐deleted subgraphs. Furthermore, as another partial result concerning the reconstruction of locally finite trees, we show that the same is true for locally finite trees whose set of vertices of degree s is nonempty and finite (for some positive integer s).

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