四色猜想的解析论证及其在地图绘制中的应用  

Analytical proof on four color guess and mapping application.

作　　者：刘庆民[1] 欧阳富[2] 蔡汉忠[2] 

机构地区：[1]杭州电子科技大学机械学院,浙江杭州310018 [2]北华大学交通建筑工程学院,吉林吉林132013

出　　处：《浙江大学学报（理学版）》2011年第4期367-375,共9页Journal of Zhejiang University（Science Edition）

摘　　要：依据欧拉定理,研究了边数差和着色数计算公式,对四色猜想进行了研究.借助四面体顶点数与面积数相等的原则、多面体边数不变的原则和多余理论,用边数差数学计算方法论证了四色猜想.用简单的数学公式和几何作图方法说明了四色猜想的合理性,为其提供了可靠的理论依据.用"三色包点"和"以面切体"的几何作图法,证明多面体和平面地图的着色数恒为4;非三色包点的图形,可以通过"以面切体"的方法转换成三色包点的图形;使用多余国家、多余边数的数学技巧代替计算机使用的不可避免性、可约性是合适的.理论分析及实例论证表明该方法简单可行.Developed formulae of edge difference and coloring number, discussed four color guess by the Euler theo- rem. By the aid of the principle that acme number of tetrahedron is equal to its area number, and edge number is changeless, as well as superabundance theoery, demonstrated four color guess by edge difference method. Explained the rationality of four-color guess by mathematics formula and simple geometry method, and offered the reliable the- oretical foundation for it. Colord numbers of polyhedron and plane map identically equal to 4 are proved by the meth- od of ＂three colors enveloped point＂ and ＂body formed by surface ＂ figure with no ＂three colors enveloped point＂ can be changed to figure with ＂three colors enveloped point＂; It is avalable that superabundance country and supera- bundance edge number are using to replace inescapability and reducibility sued by computer. Theory analysis and ex-amples argumentation indicated this method simple and feasible.

关 键 词：四色猜想 边数差计算公式 多余边数 四色猜想证明式 等值原则 

分 类 号：O141.2[理学—数学]