A counterexample to the reconstruction conjecture for locally finite trees

Autor:	Bowler, Nathan, Erde, Joshua, Heinig, Peter, Lehner, Florian, Pitz, Max
Rok vydání:	2016
Předmět:	Mathematics - Combinatorics
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
Externí odkaz:	http://arxiv.org/abs/1606.02926 Zobrazit plný text záznamu View this record from Arxiv