华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (2): 17-21.

• 应用数学与基础数学 • 上一篇    下一篇

Cm,n的最小亏格与Km,n的强嵌入

镡松龄 任 韩   

  1. 华东师范大学 数学系, 上海 200241
  • 收稿日期:2010-07-01 修回日期:2010-10-01 出版日期:2011-03-25 发布日期:2011-03-25
  • 通讯作者: 镡松龄

Genus of Cm,n and strong genus embedding of Km,n

SHAN Song-ling, REN Han   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2010-07-01 Revised:2010-10-01 Online:2011-03-25 Published:2011-03-25
  • Contact: SHAN Song-ling

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摘要： 令Cm,n表示长为m的圈与n个孤立点的联结(join)所得的图. 本文证明了Cm,n的最小亏格和
最小不可定向亏格与完全二部图Km,n的相等. 同时，证明当m≥2并且n≥2时, Km,n在其最小可定向曲面上有一个强嵌入; 当m≥3并且n≥3,时, 在最小不可定向曲面上有一个强嵌入.

关键词: 亏格, 不可定向亏格, 强嵌入, 亏格, 不可定向亏格, 强嵌入

Abstract: Let Cm,n be the join graph of Cm(a cycle of ength m) and n isolated vertices. In this paper, we first show hat the genus and nonorientable genus of Cm,n equal those of Km,n, which were well known and discovered by Ringel [1, 2].
Then we show that the complete bipartite graph Km,n has a strong orientable genus embedding if m≥2 and n≥2 and has a strong nonorientable genus embedding if m≥3 and n≥3.

Key words: nonorientable genus, strong embedding, genus, nonorientable genus, strong embedding

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