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“四色猜想”研究

FOUR COLOUR CONJECTURE
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摘要 “四色猜想”提出至今将近150 年,百年来它吸引了众多数学家们。1976年美国数学家Appel 和Haken 宣布:他们用电子计算机花了1200 多小时证明了“四色猜想”是成立的。但人们仍期待着一个简单的理论证明,况且据说后来有人指出了计算机证明的一些漏洞。总之,“四色猜想”至今尚未完全解决,故有继续研究之必要。通过极大平面图的结构研究,提出了构造极大平面图的3 种方法,即“加点法”、“删点法”与“任意法”。建立了一个理论系统,包括11 个定义、12 个命题及7 个定理。采用“平行归纳法”证明了极大平面图可四着色,从而证明对于极大平面图“四色猜想”是对的。 It has been nearly 150 years since Four color conjecture was advanced,which has attracted many mathematicians for a hundred of years.Though American mathematician Appel and Haben declared that they had proved Four color conjecture to be correct by using computers,which ran for 1200 hours,people still expect a simple theoretical proof instead of using computer.What's more,it is said that someone has ever pointed out that there are some mistakes in the computer proof.In general,Four color conjecture is still not solved completely until now, so it is necessary to coninue the research.Through a study on the maximum planar graph,three methods are proposed,which constructe the maximum planar graph,i.e.the points added method,the points deleted method and the arbitary method.From these methods a theoretical system is established.It includes 11 definitions,12 sentences and 7 theorems.With the parallel inductive method,it proved the maximum planar graph can be colored by 4 colors.As a result,the four color conjecture is correet.
作者 王绍文
出处 《北京机械工业学院学报》 1999年第4期29-32,共4页 Journal of Beijing Institute of Machinery
关键词 平面图 极大平面图 同构图 点色数 四色猜想 planar graph maximum planar graph isologous graph point color number
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