On complementary cycles in locally semicomplete digraphs
type: Item
instance of: scholarly article
title: On complementary cycles in locally semicomplete digraphs
zbMATH Open document ID: 0816.05036
DOI: 10.1016/0012-365X(93)E0099-P
author: Yubao Guo
author: Lutz Volkmann
published in: Discrete Mathematics
publication date: 1995-02-01T00:00:00Z
review text: A digraph \(D\) is locally semicomplete if for each vertex \(x\) in \(D\) the subdigraphs induced by the positive and negative neighbor sets of \(x\) are both semicomplete. This paper gives the following result about 2- connected locally semicomplete digraphs: Such digraphs do not have their vertex set partitioned by two complementary dicycles if and only if they are 2-diregular and have odd order. From this theorem follow two conjectures of Bang-Jensen giving conditions for a 2-connected local tournament \(D\) to have a dicycle \(C\) such that \(D- V(C)\) is strong.
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 716452
zbMATH Keywords: complementary cycles
zbMATH Keywords: dicycle cover
zbMATH Keywords: locally semicomplete digraphs
zbMATH Keywords: tournament
zbMATH Keywords: dicycle
reviewed by: Norman F. Quimpo
MaRDI profile type: Publication
cites work: Locally semicomplete digraphs: A generalization of tournaments
cites work: On the structure of locally semicomplete digraphs
cites work: Q4201932
cites work: On Subtournaments of a Tournament
cites work: Q3691764
cites work: Complementary cycles of all lengths in tournaments
Wikidata QID: Q126778368
description: scientific article; zbMATH DE number 716452