有向图在可定向曲面上的嵌入性

Embeddable Properties of Digraphs in Orientable Surfaces

Bonnington,Conder和Morton在2002年给出了有向图嵌入亏格的基本性质,并提出了如下问题:如何刻划有向嵌入是上可嵌入的?是否存在类似刻划图的上可嵌入中使用的可裂树的结果?受此问题的启发,本文给出了一类有向图在可定向曲面上是上可嵌入的性质.作为直接推论,可得到已有的反棱境图是上可嵌入的结论.另外得到了一些新的上可嵌入的图类.

In 2002, Bonnington, Conder and Morton gave the problem： ＂Characterize those embedding digraphs which are upper-embeddable. Is there an analogue to the splitting tree result used to classify upper-embeddale graphs？＂ Motivated by this problem, in this paper, we give an upper-embeddable property of one kind of digraphs in orientable surfaces. As the directive corollary, the known embedding maximal genera of the antiprisms can be gotten. Further more some new kinds of upper-embedding digraphs are gotten.