珍珠湾ART

标题: 无穷地图的四色问题 [打印本页]

作者: fzy 时间: 2005-9-15 23:30
标题: 无穷地图的四色问题

难度：++

对平面上有限多个国家的地图进行染色，4种颜色就够了。现在假设平面上有无穷多个国家G1，G2，G3，。。。，每个国家可能和无穷多个其他国家接壤。4种颜色还够不够？

作者: Jenny 时间: 2005-9-16 01:42
标题: 回复：无穷地图的四色问题

够了

作者: QL 时间: 2005-9-16 04:52
标题: 回复：无穷地图的四色问题

Let's denote H4 ={G1, G2, G3, G4}; H5={G1,G2,..,G5}.....

Obviously a soultion to H5, confined on H4 will also be a solution of H4. We can also say that this restricted solution on H4 can be 'extended' to H5.

We can show the following:

(1)if a solution of H4 can be extended to Hm (m>=5) then it can be extended to H5,H6,...Hm

(2)There is at least one solution of H4 that can be extended to any Hm (m>4), let's pick one of such a solution, S4=(C1,C2,C3,C4), where the Ci's are the colors for each country of H4.

Now, move to H5, by similar argument we can prove that, we can pick a color C5, so that S5=(C1,C2,C3,C4,C5) can be extened to H6,H7, .....

and so on.....

作者: fzy 时间: 2005-9-16 19:25
标题: 回复：回复：无穷地图的四色问题

Care to tell us why, 观音姐姐? (Why did he call you 观音姐姐? )

作者: fzy 时间: 2005-9-16 19:25
标题: Idea right, statement can be simpler.

Idea right, statement can be simpler.

作者: Jenny 时间: 2005-9-16 19:30
标题: 回复：回复：回复：无穷地图的四色问题

我也不知为什么，可能是我冤枉了他吧。

欢迎光临珍珠湾ART (http://zzwav.com/)