最大平面图G_M的孪生图G_M^T和对角线变换DT

The Twin Graph G_M^T of Maximal Plane Graph G_M and Diagonal Transformation DT

提出了最大平面图G_M的孪生图G_M^T和"孪生图对"的概念和定义,探讨了"孪生图对"的特性,分析了"孪生图对"的四色着色方案彼此间的关系,并由此形成了最大平面图着色的"对角线变换法".文中以二个实例("正二十面体的平面嵌入图";"Appel和Haken的例子")验证了研究的结果,同时也显示了孪生图G_M^T可被应用的场合及其实用性.

This paper presents concepts and definitions of twin graph GTand ＂twins＂ （twin graph pair） of maximal plane graph GM, explores properties of ＂twins＂, and analyses relations between Four-colorings of ＂twins＂. In this paper, ＂method of diagonal transformation＂ for Four-coloring in maximal plane graph is given,results of studies are testified, and applications of ＂twins＂ are showed by two practical examples （＂graph embedded in plane on regular icosahedron （Twenty-Face-Body）＇; ＂Appel and Haken＇s Example＂）.