A Note on Directed Genera of Some Tournaments  

作　　者：Jian-bing LIU Rong-xia HAO 

机构地区：[1]Department of Mathematics, Beijing Jiaotong University

出　　处：《Acta Mathematicae Applicatae Sinica》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)

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）.

关 键 词：DIGRAPH directed embedding directed genus surfaces 

分 类 号：O157.5[理学—数学]