The automorphism group of the random graph: four conjugates good, three conjugates better.
type: Item
instance of: scholarly article
title: The automorphism group of the random graph: four conjugates good, three conjugates better.
zbMATH Open document ID: 1058.20003
DOI: 10.1016/S0012-365X(02)00692-1
published in: Discrete Mathematics
publication date: 2003-07-29T00:00:00Z
review text: The random graph (or countable universal graph) \(R\) is the unique countable graph whose vertex set \(V(R)\) is the union of two sets \(P,Q\) such that \(P\cap Q=\emptyset\) and there exists a vertex \(u\in V(R)-(P\cup Q)\) adjacent to all vertices from \(P\) and to none from \(Q\). Let the automorphism group of \(R\) be \(G\). In 1995, the present author published the proof that if \(\sigma\) and \(\tau\) are non-identity elements of \(G\), then \(\tau\) may be written as the product of five conjugates of \(\sigma\). Then M. Rubin improved this number to four. In this paper, the author improves it to three.
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1956043
zbMATH Keywords: conjugates
zbMATH Keywords: random graph
zbMATH Keywords: automorphism groups
author: John K. Truss
reviewed by: Bohdan Zelinka
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1956043