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On the reconstruction of locally finite trees
Author(s) -
Andreae Thomas
Publication year - 1981
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190050202
Subject(s) - mathematics , combinatorics , vertex (graph theory) , isomorphism (crystallography) , integer (computer science) , subdivision , finite set , degree (music) , tree (set theory) , discrete mathematics , set (abstract data type) , graph , mathematical analysis , chemistry , physics , archaeology , computer science , history , crystallography , acoustics , crystal structure , programming language
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 ).