Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface
Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface
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DOI：
10.1090/s0002-9947-1991-1040045-3
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发表时间：
1991-02
影响因子：
1.3
通讯作者：
C. Thomassen
中科院分区：
文献类型：
--
作者：
C. Thomassen
我们描述了所有的定期领带的环面和克莱因瓶。我们应用这一点来描述，为每个定向（分别nonorientable）表面S，所有（但不多）顶点传递图，可以画在S上，但不是在任何表面较小的属（分别crosscap数）。特别地，我们证明了巴拜的猜想：对每个g > 3，亏格g的点传递图只有1000个.事实上，它们都是2阶的，作用在亏格g表面上的群只有100多个。我们还导出了一个不可定向的Hurwitz定理。
We describe all regular tiings of the torus and the Klein bottle. We apply this to describe, for each orientable (respectively nonorientable) surface S, all (but finitely many) vertex-transitive graphs which can be drawn on S but not on any surface of smaller genus (respectively crosscap number). In particular, we prove the conjecture of Babai that, for each g > 3, there are only finitely many vertex-transitive graphs of genus g. In fact, they all have order 2, there are only finitely many groups that act on the surface of genus g . We also derive a nonorientable version of Hurwitz' theorem.