多面体平图的4着色方法  

4-Colouring Method of the Polyhedron Plane

作　　者：万禧[1] 李晓毅[2] 

机构地区：[1]安徽理工大学土木建筑学院,安徽淮南232001 [2]沈阳师范大学数学与系统科学学院,辽宁沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2010年第2期137-140,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10471096)

摘　　要：讨论了多面体平图的4着色问题,将平图的面着色问题简化为平图面中心的顶点着色问题。提出了多面体4着色的基本思路,当顶点数p值很大并且有许多面交汇时,实现对偶图的顶点4着色问题借助于对偶图G(p,q,f)的两棵对偶树的分解,而对偶图G(p,q,f)两棵对偶树的分解又依靠对偶图G′(f,s,t)的Hamilton路径p的分解。概括了对偶图G(p,q,f)4着色的基本方法,同时在此基础上给出了8面体,12面体,20面体,32面体4着色的具体步骤,并以图形的形式给出了以上多面体4着色的具体方案。The article discusses the problem of 4-coloring for the polyhedral plane,simplifying the problem of surface coloring of the plane to the problem of vertex coloring to the center of the plane surface.The basic idea of 4-coloring for the polyhedral plane is described,when the top-points value p is significanty large and many plane intersect,to achieve the dual plane vertex 4-coloring problem by means of two pairs dual tree decomposition for the dual plane G（p,q,f）,which is depend on the decomposition of Hamilton path p for the dual plane G′（f,s,t） of the plane G（p,q,f）;This paper summarizes the basic methods of 4-coloring the dual plane G（p,q,f）,then on this basis and at the same time,the specific steps of 4-coloring to the octahedral,dodecahedron,icosahedrons,32 polyhedral are introduced,finally the specific program of above kind polyhedrals 4-coloring are presented graphically.

关 键 词：对偶图 对偶树 Hamilton路径 4着色 

分 类 号：O157[理学—数学]