吴小宁

（  无锡市委办公室,无锡　214131 ；  ）

摘要： 二叉树对着色问题(CPBT)是四色问题的等价命题. 化变是一种特殊的映射, 其定义域为某个非空集的幂集. 我们讨论了化变的基本性质并确立了化变论的初步框架. 经专门处里后, CPBT可转化为给定3元集对16种基本化变的稳定性问题. 引入辅助化变后, 基本化变的数目还可进一步减少为4. 我们证明CPBT在某些特殊情况下成立, 改进了已知结论.
关键词： 化变, 四色定理, 二叉树对

Wu Xiaoning

（  Wuxi municipal party committee office, Wuxi 214131 ；  ）

Abstract： The problem of Colouring Pairs of Binary Trees(CPBT) is equivalent to Four Colour Theorem. A huabian is a special mapping which domain must be the power set of a nonempty set. We discussed the basic properties of huabian, and established the preliminary framework of huabian theory. After special treatment, CPBT can be turned to the stability of a given set containing 3 elements on the collection of 16 huabians. By introducing some auxiliary huabians, the number of necessary Huabians can reduce to 4. We proved that CPBT is established in some particular cases. This improves the known results.
Keywords： huabian, Four Color Theorem, Pairs of Binary Trees

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