基于传统逻辑简捷证明四色问题研究

Study on the Four-color Problem of Simple Proof Based on Traditional Logic

分析四色问题难点,采用构形法、点着色扩展法和点染色公式法等三种新方法,简捷证明四色问题成立。三种证法,均采用数形结合的数学方法,但思路各异。其中尤以点染色公式法,思维逻辑新颖,论述简朴。四色溯源,当属欧拉公式V-E+F=2及其导出的平面图最小度δ≤5和点染色公式V=2+E/3,均是重要关注点,其中欧拉公式应是四色问题的渊源。

The difficulty of the four-color problem is analyzed,and three new methods such as configuration method,point coloring extension method and point coloring formula method are adopted to prove the validity of the four-color problem.The three proofs all adopt the mathematical method of combining numbers and shapes,but their ideas are different.In particular,the point dyeing formula method is novel in logic and simple in discussion.The origin of four colors is Euler’s formula V-E+F=2,the minimum degree of plane graphδ≤5 derived from it and the point dyeing formula V=2+E/3,both of which are important concerns.Euler’s formula should be the origin of four colors.