Imrich, Wilfried and Smith, Simon M.
(2017)
On a theorem of Halin.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 87
(2).
pp. 289297.
ISSN 00255858
Preview 

PDF
Imrich Smith On a theorem of HalinPublishedVersion.pdf
 Whole Document
325kB 
Item Type:  Article 

Item Status:  Live Archive 

Abstract
This note presents a new, elementary proof of a generalization of a theorem of Halin to graphs with unbounded degrees, which is then applied to show that every connected, countably infinite graph $G$, with $\aleph_0 \leq \A(G) < 2^{\aleph_0}$ and subdegreefinite automorphism group, has a finite set $F$ of vertices that is setwise stabilized only by the identity automorphism. A bound on the size of such sets, which are called {\em distinguishing}, is also provided.
To put this theorem of Halin and its generalization into perspective, we also discuss several related nonelementary, independent results and their methods of proof.
Repository Staff Only: item control page