Non-reconstructible locally finite graphs

Autor:	Bowler, Nathan, Erde, Joshua, Heinig, Peter, Lehner, Florian, Pitz, Max
Rok vydání:	2016
Předmět:	Mathematics - Combinatorics
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
Externí odkaz:	http://arxiv.org/abs/1611.04370 Zobrazit plný text záznamu View this record from Arxiv