四色定理

通过最大平面图和四色猜想的介绍及对最大平面图着色的分析，揭示了最大平面图着色是四色定理普遍证明的核心。

By introducing maximal planar graph and the conjecture of four color , as well as analyzing the coloring of maximal planar graph , it is revealed that the coloring of maximal planar graph is the core of the four color theorem .

使用四色定理求解图形着色的数学模型

The Mathematical Model of Solving Graph Coloring by Four-color Theorem

四色定理和Ramsey定理基于模型论的证明

The Proofs of Four Colours and Ramsey Theorem s Based on Model Theory

四色定理和Ramsey定理是图论中重要的定理，文章运用模型论中的紧致性定理、图象定理等将图论中的四色定理推广到无穷情形，并给出了Ramsey定理基于模型论方法的证明。

Four colours theorem and Ramsey theorem are very important theorems in graph theory . Exploiting compact theorem and diagram theorem , the paper extends four colours theorem to infinite case and introduces short proof for Ramsey theorem based on model theory method .

这就是四色定理论证的关键。

This is also a key to proof the 4-color theorem .

本文论述与四色定理等价的几个新命题。

Several propositions equivalent to the four colour theorem are discussed .

地图四色定理的非计算机证明

The Prove of The Four-color Problem of a Map without a Computer

与四色定理有关的一些结果

Some results related to the four colour theorem

四色定理论证

Proof of the 4 - Color Theorem

标准四色定理中所用到的边界定义方式与常识相同，排除了哈德逊地图这类诡异的情况。

The standard four-color theorem defines borders in a way that hews to common sense and excludes bizarre cases such as Hudson 's.

虽然在数学领域也有一些新的进展，例如对著名的四色定理的证明，1但是基本的材料却保持不变。

Although there have been some new developments in mathematics , such as the proof of the famous four-color theorem , 1 the basic material has remained unchanged .

纽曼的想法是：我们可以尝试用机器来解决一些完全不同的问题，比如四色定理，以及各类关于格和群的问题等等……

Newman 's intention was that mathematical problems of an entirely different kind from those so far tackled by machines might be tried , e.g. testing out ( say ) the 4-colour theorem or various theorems on lattices , groups , etc. ...

论述四色的由来及确切答案，并且证明了四色定理的成立。

This article discussed the origin of the colour problem and its true answer and argue the theorem of four color to set .