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A Note on Directed Genera of Some Tournaments

A Note on Directed Genera of Some Tournaments
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摘要 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. Cornbin. 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 Kn. In this paper, we use the current graph method to show that there exists a tournament, whichhas the directed genus[(n-3)(n-4)/12], on n vertices if and only if n = 3 or 7 (mod 12). 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. Cornbin. 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 Kn. In this paper, we use the current graph method to show that there exists a tournament, whichhas the directed genus[(n-3)(n-4)/12], on n vertices if and only if n = 3 or 7 (mod 12).
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2018年第3期478-484,共7页 应用数学学报(英文版)
基金 Supported by the National Natural Science Foundation of China(No.11731002) the Fundamental Research Funds for the Central Universities(Nos.2016JBM071,2016JBZ012)
关键词 DIGRAPH directed embedding directed genus surfaces digraph directed embedding directed genus surfaces
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