关于点猜想的几点注记

Some Explanations to the Dot Conjecture

在平面上给出n个点(不能共线),且任意两点之间都有直线相连,记此图为Gn.点猜想称Gn中至少有一条直线仅过两个点,文章对此结论做了几点拓展,首先证明了:n>2时,若Gn中只有一条直线仅过两个点,则一定还存在一条直线仅过三个点.接着证明了:n>3时,若Gn中只有一条直线仅过两个点,只有一条直线仅过三个点,则一定还存在一条直线仅过四个点.

The dot conjecture claims there exists a straight line in going through two dots.This paper expands this conclusion.Firstly,it proves that if there is only one straight line going through two dots in when,then there must be a straight line going through there dots.Secondly,it proves that if there is only one straight line going through two dots and only one straight line going through there dots in when,then there must be a straight line going through four dots.