关于循环图的曲面嵌入  

Embeddings of Circular Graphs

作　　者：任韩[1] 邓默[1] 

机构地区：[1]华东师范大学数学系,上海200062

出　　处：《数学物理学报（A辑）》2007年第6期1148-1154,共7页Acta Mathematica Scientia

基　　金：中国国家自然科学基金(10271048:10671073)资助

摘　　要：该文集中探讨循环图的曲面嵌入性质.决定了所有循环图的最小亏格(其中包括可定向亏格与不可定向亏格)和最大亏格.对于固定的整数l(≥3)和充分大的自然数n,只有一种方式将4-正则循环图C(n,l)嵌入到环面上使得其每一个面都是4-边形.特别地,循环图C(2l+2.l)在加入若干条新边后可以同时将环面与Klein瓶进行三角剖分.In this paper the authors investigate the embeddings of the circular graphs. The authors determine the minimum orientable genus and the minimum nonorientable genus and show that all the circular graphs are up-embeddable. The authors show that for a fixed integer l（≥ 3） and large enough n, there is only one way to embed a 4-regular circular graph C（n, l） into the torus such that each face is a quadrilateral. In particular, the authors find that both the torus and the Klein bottle may be quadrangulated by the circular graph C（2l ＋ 2, l） which, by introducing some new edges, may also triangulate both of the two surfaces.

关 键 词：循环图 嵌入 最小(不可定向)可定向亏格. 

分 类 号：O157.5[理学—数学]