摘要
《四色定理》系著名数学难题。作者摒弃了传统的证题思路,在极大平面图内构造了一类镶嵌图。以其为工具深入地挖掘了平面图的某些新的拓朴不变性;深刻地揭示了平面Hamiliton图的充要条件;避免了“不可避免完备集”的建立,及其可约性讨论的离散方法。把四色定理的证明纳入逻辑论证的轨道。依此阐明平面图4-可着色的充分性。为四色定理提供了一个简明的数学证明。全文共3部分。本文为其第1部分,构造了镶嵌图并抽象为G-镶嵌,挖掘其系统性质及存在性,为四色证明准备了有力工具。
The two worldwide puzzler in mathematics across, i, e. the proof of 'Four Color Theorem' by non -computer and the necessary - sufficient conditions of planes Hamiltonian graph, are described in the paper. Abandoning the traditional thinking of demonstration, the author constructs a kind of G△M-graph in a maximal planes graph, and from which opens up a new theory for this system.
Taking the as a means, the author deeply excavates some new topological invariances in the planes graph and pofoundly reveals that the planes graph is the necessary -sufficient conditions for Hamiltonian-graph, which avoids establishing a 'inevitable perfect set, 'and the method discussing the separation of reduciblity the proof of 'Four color Theorem' is brought into line with logical demonstration. On the basis of these, the sufficiency of the 4-col-orallcty of the plane graph, which provides a simple and clear mathematical proof for the 'Four Color Theorem'.
