与四色定理等价的几个命题  

Several Propositions Equivalent to the Four Colour Theorem

作　　者：谢力同[1] 刘桂真[1] 

机构地区：[1]山东大学数学研究所,济南250100

出　　处：《应用数学》2000年第3期59-62,共4页Mathematica Applicata

基　　金：国家自然科学基金;高等学校博士学科点专项科研基金资助课题

摘　　要：本文论述与四色定理等价的几个新命题 .从而给出了平面三角剖分及圈上的 4染色集的一些新性质 .将平面图的 4可染色问题转化为圈上的 4染色来研究 ,这将更便于用计算机来寻找关于四色定理的更简单的证明方法 ,也为探索四色定理的理论证明提供了新的途径和方法 .Several propositions equivalent to the four colour theorem are discussed. Therefore some new properties of 4 colourings of plane triangulations and circuits are given. The four colour problem of plane graphs is discussed by transforming it into a problem on 4 colourings of circuits. This is not only worthful to look into the more simple methods to prove the four colour theorem with the help of computers, but also gives new methods and walks for its theoretical proofs.

关 键 词：图 平面三角剖分 四色定理 染色 等价 命题 

分 类 号：O157.5[理学—数学]