| 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] |
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| “三色图”的一个充分条件 |
| 董晓光 |
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(系统工程与应用数学系)
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| 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: |
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| A Sufficient Condition for the 3-Chromatic Graph |
| Dong Xiaoguang |
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(Department of Applied Mathematics and System Engineering)
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| 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 |
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