A Note on Directed Genera of Some Tournaments

An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can be directed embedded. Bonnington, Conder, Morton and McKenna [J. Combin. Theory Ser....

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 34; no. 3; pp. 478 - 484
Main Authors Liu, Jian-bing, Hao, Rong-xia
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Embedding
Graph theory
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Tournaments & championships
05C25
digraph
surfaces
directed genus
O157.6
directed embedding
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Summary:An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can be directed embedded. Bonnington, Conder, Morton and McKenna [J. Combin. Theory Ser. B, 85(2002) 1-20] gave the problem that which tournaments on n vertices have the directed genus ⌈( n −3)( n −4)/12 ⌉, the genus of K n . In this paper, we use the current graph method to show that there exists a tournament, which has the directed genus ⌈( n −3)( n −4)/12 ⌉, on n vertices if and only if n ≡ 3 or 7 (mod 12).
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-018-0763-9