维多利亚时代四色定理的证明
A Victorian Age Proof of the Four Color Theorem
摘要：
本文研究了四色地图问题中的一些老问题。本文给出了构造Kempe四色定理反例的一般方法，并证明了通过重构极大可平面图的双螺旋链形式的特殊2-色双路分解，可以排除所有反例.本文的第二部分给出了三次平面映射的四色定理的一个算法证明。我们的算法证明分三步给出。前两个步骤是最大的单色，然后最大的双色着色的脸，以这样的方式，所产生的无色（白色）地区的不完整的双色地图诱导没有奇循环，使在（最后）第三步四着色的地图已获得几乎平凡。
英文摘要：
In this paper we have investigated some old issues concerning four color map problem. We have given a general method for constructing counter-examples to Kempe's proof of the four color theorem and then show that all counterexamples can be rule out by re-constructing special 2-colored two paths decomposition in the form of a double-spiral chain of the maximal planar graph. In the second part of the paper we have given an algorithmic proof of the four color theorem which is based only on the coloring faces (regions) of a cubic planar maps. Our algorithmic proof has been given in three steps. The first two steps are the maximal mono-chromatic and then maximal dichromatic coloring of the faces in such a way that the resulting uncolored (white) regions of the incomplete two-colored map induce no odd-cycles so that in the (final) third step four coloring of the map has been obtained almost trivially.
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