引用本文: | 董晓光.“三色图”的一个充分条件[J].国防科技大学学报,1989,11(2):29-32.[点击复制] |
Dong Xiaoguang.A Sufficient Condition for the 3-Chromatic Graph[J].Journal of National University of Defense Technology,1989,11(2):29-32[点击复制] |
|
|
|
本文已被:浏览 5144次 下载 4942次 |
“三色图”的一个充分条件 |
董晓光 |
(系统工程与应用数学系)
|
摘要: |
文中证明了定理:若图 G 中不存在与 K4同胚的子图,则其色数X(G)≤3。进而得到三色图的一个充分条件。只要能证明与上述定理类似的一个定理:“若图G中不存在与K5同胚的子图,则其色数X(G) ≤4”,则世界著名的“四色猜想(4CC)”即得证。 |
关键词: 图论,三色图,充分条件 |
DOI: |
投稿日期:1988-08-08 |
基金项目: |
|
A Sufficient Condition for the 3-Chromatic Graph |
Dong Xiaoguang |
(Department of Applied Mathematics and System Engineering)
|
Abstract: |
The following theorem has been proved in this paper:“the chromatic number X(G)≤3 if the graph G has no subgraph homeomorphic to K4”,thus further getting a sufficient condition for the 3-chromatic graph. So long as the theorem similar to the above one:“the chromatic number X (G)≤4 if the graph G has no subgraph homeomorphic to K5”can be proved,the famous“4 colour conjecture (4CC)”in the world will be confirmed. |
Keywords: graph theory,3-chromatic graph,sufficient condition |
|
|