四色定理论证

Proof of the 4-Color Theorem

用离散数学之图论证明"四色猜想",巧妙而深层次地应用数学归纳法和换色法,解决了肯泊(A.Kempe)百多年前提出"不可避免构形集"中的一个地域有五个邻域的情况的所谓"可约性"问题,同时指出了1890年希伍德(P.Heawood)举出的25阶反例(当时,他以此说明"四色猜想"不成立,而"五色定理"成立)与本文中的一种可换色(即"可约性")的典型实例类同,进而简捷而理想地证明了"四色猜想"是成立的,使"四色定理"得到科学的论证。

Prove the 4-color conjecture by graph theory in the discrete mathematics. By skillfully using mathematics induction and interchanging-colors, this article successfully solves the simplifying prohlem advanced by A. Kempe more than one hundred years ago, which says there exists the region adjacent to five neighboring regions in the unavoidable structures group. Besides, the artide points out that, the example of the 25 orders illustrated by P. Heawood in 1890, which shows a 5-color theorem is correct, while the 4-color conjecture is not, is similar to a typical illustration in the article. But different from the former, the article simply and ideally infers that the 4-color problem holds by making full use of the illustration in interchanging colors. That shows the proof in the article is complete and scientific.