简评四色定理的一种非计算机“逻辑证明”  

A brief comment on a non-computer "logical proof" of the four-color theorem

作　　者：杨军 李高平 李庆 YANG Jun;Ll Gao-ping;LI Qing(School of Mathematics,Southwest Minzu University,Chengdu 610041,China)

机构地区：[1]西南民族大学数学学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2021年第3期326-329,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金青年基金项目(11401493);西南民族大学中央高校基本科研业务费专项资金项目(2020NYB17)。

摘　　要：2020年,Y. Wang基于构形和可归约性的经典概念提出了一份四色猜想(The Four Color Conjecture, 4CC)的归谬法证明.首先构造反例指出其"临界k色图"定义的一个缺陷.其次对比分析表明,把"最小图"改为"临界5色图"的做法产生了逻辑二难困境:若按前者对待,则原文尚缺论证能够抵抗传统的Heawood图的反例攻击;若按后者处理,则当今图论无法保证其存在性.In 2020, Y. Wang proposed a proof by contradiction of the Four Color Conjecture(4 CC) based on the two classic concepts of configuration and reducibility. This article first constructs a counterexample to point out a defect in the definition of "critical 5-chromatic graph". Secondly, the comparative analysis shows that the practice of changing the "minimal graph" to the "critical 5-chromatic graph" has begot a logical dilemma: If it is treated as the former, then the original still lacks the proof that it can resist the counterexample attack of the traditional Heawood graph;if it is dealt with as the latter, then the contemporary graph theory cannot guarantee its existence.

关 键 词：四色猜想 极大平面图 最小图 临界k-色图 Heawood图 

分 类 号：O157.5[理学—数学]