Non-reconstructible locally finite graphs
Autor: | Bowler, Nathan, Erde, Joshua, Heinig, Peter, Lehner, Florian, Pitz, Max |
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Rok vydání: | 2016 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | Two graphs $G$ and $H$ are \emph{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 \emph{reconstructible} if $H \cong G$ for all $H$ hypomorphic to $G$. Nash-Williams proved that all locally finite graphs with a finite number $\geq 2$ of ends are reconstructible, and asked whether locally finite graphs with one end or countably many ends are also reconstructible. In this paper we construct non-reconstructible graphs of bounded maximum degree with one and countably many ends respectively, answering the two questions of Nash-Williams about the reconstruction of locally finite graphs in the negative. Comment: Figure 1 updated and minor typographical errors corrected |
Databáze: | arXiv |
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