关于四色问题的P.J.Heawood反例

英国数学家Ｋａｍｐｅ给出了四色定律的第一个证明，１０年后Ｈｅａｗｏｏｄ指出该证明有致命错误，Ｈｅａｗｏｏｄ还利用Ｋａｍｐｅ的方法证明了五色定理。本文分析了Ｋａｍｐｅ方法的漏洞，同时也分析了Ｋａｍｐｅ方法的潜在威力，为此，引入“Ｋａｍｐｅ链”的概念，并把它用到四色问题的几类特殊情况的证明。简化了Ｈｅａｗｏｏｄ反例，分析了反例的逻辑结构。

On the Heawood's Couterexample of Four Color Problem

Britain mathematician Kempe gave the first proof of the four color theorem in 1879.Afterten years Heawood pointed that there was a fatal mistake in the proof of Kempe. This was a famousevent in mathematical history. In this paper we look back to the history. Although Kempe made amistake , his idea on solution of the four color problem is very useful to study the problem to going stepfurther .We introduce the Kempe chain and discuss several special cases using it. Moreover we simplify the counterexample of Heawood. In this way we find some interesting results.