四色定理经典证明的蓝图
Blueprint for a Classic Proof of the Four Colour Theorem
摘要：
证明使用的性质，三角形的可平面图的顶点可以是四种颜色，如果三角形可以有一个+1或-1的方向，使三角形的方向和周围的每个顶点是3的倍数。这种定向首先被单独地用于由具有v个顶点的三角化可平面图中的Hamilton回路产生的两个三角化多边形中的一个。然后通过逐个添加另一个多边形的三角形来重建图形。当图被完全重构时，三角形的方向总是有一个组合，使得它们围绕汉密尔顿回路中的v-2个连续顶点中的每一个的和是3的倍数。然后可以证明，围绕剩余两个顶点的三角形方向之和也必须是3的倍数。
英文摘要：
The proof uses the property that the vertices of a triangulated planar graph can be four coloured if the triangles can have a +1 or -1 orientation so that the sum of the triangle orientations around each vertex is a multiple of 3. Such orientation is first used separately on one of the two triangulated polygons resulting from a Hamilton circuit in a triangulated planar graph with v vertices. The graph is then reconstructed by adding the triangles of the other polygon one by one. When the graph is totally reconstructed there is always a combination for the orientations of the triangles for which their sum around each of v-2 successive vertices in the Hamilton circuit is a multiple of 3. It is then provable that the sum of the triangle orientations around the two remaining vertices must also be a multiple of 3.
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