Different vertices are colored in a plan. Adjacent vertices are colored dif-ferently from nonadjacent vertices, which are colored the same color. One color is used for a single point, two colors are used for points wi...Different vertices are colored in a plan. Adjacent vertices are colored dif-ferently from nonadjacent vertices, which are colored the same color. One color is used for a single point, two colors are used for points without a loop, and a maximum of four colors are used for points with a loop. A maximum of four colors are used to color all points. .展开更多
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&q...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.展开更多
This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral w...This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture.展开更多
文摘Different vertices are colored in a plan. Adjacent vertices are colored dif-ferently from nonadjacent vertices, which are colored the same color. One color is used for a single point, two colors are used for points without a loop, and a maximum of four colors are used for points with a loop. A maximum of four colors are used to color all points. .
文摘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.
文摘This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture.
