Whitney's 2-switching theorem, cycle spaces, and arc mappings of directed graphs
type: Item
instance of: scholarly article
title: Whitney's 2-switching theorem, cycle spaces, and arc mappings of directed graphs
zbMATH Open document ID: 0667.05028
DOI: 10.1016/0095-8956(89)90050-6
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: The author establishes a directed analogue of Whitney's 2-switching theorem which he uses in investigating the cycle space of tournaments. Let \(\pi\) denote a bijection between the arc-sets of two tournaments T and \(T'\). It is shown, among other things, that if T and \(T'\) are strong and \(\pi\) and \(\pi^{-1}\) preserve 4-cycles, then T and \(T'\) are isomorphic or anti-isomorphic; and if T and \(T'\) are \(10^{15}\)- connected and \(\pi\) and \(\pi^{-1}\) preserve Hamilton cycles, then \(\pi\) is induced by an isomorphism or an anti-isomorphism of T onto \(T'\).
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 4091536
zbMATH Keywords: arc mappings
zbMATH Keywords: cycle space
zbMATH Keywords: tournaments
zbMATH Keywords: isomorphism
zbMATH Keywords: anti-isomorphism
author: Carsten Thomassen
reviewed by: J. W. Moon
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90050-6
OpenAlex ID: W2067852932
cites work: Q3872493
cites work: Cycles in digraphs– a survey
cites work: Cycles through specified vertices of a graph
cites work: Arc Mappings and Tournament Isomorphisms
cites work: Long cycles generate the cycle space of a graph
cites work: Q3956975
cites work: Q4100106
cites work: On the number of Hamiltonian cycles in tournaments
cites work: Planarity and duality of finite and infinite graphs
cites work: Duality of infinite graphs
cites work: Q3337490
cites work: On Whitney's 2‐isomorphism theorem for graphs
cites work: How to Draw a Graph
description: scientific article; zbMATH DE number 4091536