研究四色问题的意义及理论构想

四色问题又称四色猜想，是世界近代三大数学难题之一．1976年两位美国数学家Appel与Haken借助计算机给出了一个证明．时至今日，四色问题的正确性早已得到数学界所承认．但是围绕它的非计算机证明，在近几十年来涌现出了各种不同的研究成果．一方面丰富了图论的内容，另一方面又促进了图的染色理论的发展．本文从研究四色问题的意义出发；揭示了四色问题所隐藏的深刻规律，在此基础上提出了一个比四色问题更具有广泛意义的理论构想．主要目地为四色问题的非计算机证明提供一个研究方向．

The Significance of Study the Four-color Map Problem and a More General Conjecture

The Four-color Map Problem is one of the world most difficult mathematical problems.It was positively proved in 1976 by two American mathematicians,Appel and Haken,with the aid of computers.However,a pure mathematical proof of the Four-color Map Theorem is as yet desired.The way to seek such a proof is really very hard.This paper will tell the stories of the problem,reveal its profound significance,and moreover,give a more general conjecture concerning the chromatic number and thickness of a graph which takes the Four-color Map Problem as a special case.