中国老鼠问题与G(p,q,f)的4着色

The Chinese Mouse Problem and 4-coluring of G(p,q,f)

提出了中国老鼠问题.阐明了求解中国老鼠问题的基本思路.发现了基于森林Fi分解的对偶图的顶点4着色方法.提出了森林Fi分解的三种方法.介绍了对偶图G(p,q,f)的A区和B区的划分,森林Fi的分解,以及对偶图G′(f,q,p)的H路径Pi的分解和G(p,q,f)的顶点4着色.讨论了H路径Pi的个数,森林Fi的个数.G(p,q,f)的4着色方案数及A区和B区的划分方案数.

The Chinese mouse problem and the basic consept of solving the Chinese mouse problem are described. The method of 4-coluring the vertics of dual on the basis of decomposition into a forest Fi is discovered. Three methods of decomposition into a forest are proposed. The division of dual G（p,q, f） into area A and area B, the decomposition of dual G（p,q,f） into a forest, the decomposition of dual Gr （f,q,p） into Harniltonian path Pi and 4-colouring the vertices of G（p,q,f） are presented. The number of hamiltonian path Pi, the number of forest F/and the number of schemes of 4-colouring G（p,q, f） are discussed.