CYCLE SPACES OF GRAPHS ON THE SPHERE AND THE PROJECTIVE PLANE  

作　　者：任韩 刘彦佩 马登举 卢俊杰 

机构地区：[1]Department of Mathematics Bast. China Normal Uiversity, Shanghai 200062, China [2]Department of Mathematics Northern Jiaoiong University, Beijing 100044, China [3]Department of Mathematics East China Normal Uiversity, Shanghai 200062, China

出　　处：《Acta Mathematica Scientia》2005年第1期41-49,共9页数学物理学报（B辑英文版）

基　　金：ShanghaiPriorityAcademicDisciplineSupportedbyNNSFofChina(10271048)SupportedbyNNSFofChina(60373030,19831080)

摘　　要：Cycle base theory of a graph has been well studied in abstract mathematical field such matroid theory as Whitney and Tutte did and found many applications in prat-ical uses such as electric circuit theory and structure analysis, etc. In this paper graph embedding theory is used to investigate cycle base structures of a 2-(edge)-connected graph on the sphere and the projective plane and it is shown that short cycles do generate the cycle spaces in the case of 'small face-embeddings'. As applications the authors find the exact formulae for the minimum lengthes of cycle bases of some types of graphs and present several known results. Infinite examples shows that the conditions in their main results are best possible and there are many 3-connected planar graphs whose minimum cycle bases can not be determined by the planar formulae but may be located by re-embedding them into the projective plane.Cycle base theory of a graph has been well studied in abstract mathematical field such matroid theory as Whitney and Tutte did and found many applications in prat-ical uses such as electric circuit theory and structure analysis, etc. In this paper graph embedding theory is used to investigate cycle base structures of a 2-(edge)-connected graph on the sphere and the projective plane and it is shown that short cycles do generate the cycle spaces in the case of 'small face-embeddings'. As applications the authors find the exact formulae for the minimum lengthes of cycle bases of some types of graphs and present several known results. Infinite examples shows that the conditions in their main results are best possible and there are many 3-connected planar graphs whose minimum cycle bases can not be determined by the planar formulae but may be located by re-embedding them into the projective plane.

关 键 词：Cycle base facial cycle graph embedding 

分 类 号：O185[理学—数学]