A counterexample to the reconstruction conjecture for locally finite trees
Autor: | Bowler, Nathan, Erde, Joshua, Heinig, Peter, Lehner, Florian, Pitz, Max |
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Rok vydání: | 2016 |
Předmět: | |
Druh dokumentu: | Working Paper |
DOI: | 10.1112/blms.12053 |
Popis: | Two graphs $G$ and $H$ are hypomorphic if there exists a bijection $\varphi \colon V(G) \rightarrow V(H)$ such that $G - v \cong H - \varphi(v)$ for each $v \in V(G)$. A graph $G$ is reconstructible if $H \cong G$ for all $H$ hypomorphic to $G$. It is well known that not all infinite graphs are reconstructible. However, the Harary-Schwenk-Scott Conjecture from 1972 suggests that all locally finite trees are reconstructible. In this paper, we construct a counterexample to the Harary-Schwenk-Scott Conjecture. Our example also answers four other questions of Nash-Williams, Halin and Andreae on the reconstruction of infinite graphs. Comment: 19 pages, Colour figures |
Databáze: | arXiv |
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