| A 3-color Theorem on Plane Graphs without 5-circuits |
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| 作者姓名： | Bao Gang XU |
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| 作者单位： | School of Math. ＆ Computer Science, Nanjing Normal University, Nanjing, 210097, P. R. China |
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| 基金项目： | Supported partially by NSFC 10001035 and 10371055 |
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| 摘 要： | In this paper, we prove that every plane graph without 5-circuits and without triangles of distance less than 3 is 3-colorable. This improves the main result of Borodin and Raspaud Borodin, O. V., Raspaud, A.： A sufficient condition for planar graphs to be 3-colorable. Journal of Combinatorial Theory, Ser. B, 88, 17-27 （2003）], and provides a new upper bound to their conjecture.
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| 关 键 词： | 平面图 回路 色彩 三色理论 |
| 收稿时间： | 30 November 2004 |
| 修稿时间： | 2004-11-302005-06-14 |
A 3-color Theorem on Plane Graphs without 5-circuits |
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| Bao Gang XU.A 3-color Theorem on Plane Graphs without 5-circuits[J].Acta Mathematica Sinica,2007,23(6):1059-1062. |
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| Authors: | Bao Gang Xu |
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| Institution: | (1) School of Math. & Computer Science, Nanjing Normal University, Nanjing, 210097, P. R. China |
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| Abstract: | In this paper, we prove that every plane graph without 5-circuits and without triangles of
distance less than 3 is 3-colorable. This improves the main result of Borodin and Raspaud Borodin, O.
V., Raspaud, A.: A sufficient condition for planar graphs to be 3-colorable. Journal of Combinatorial
Theory, Ser. B, 88, 17–27 (2003)], and provides a new upper bound to their conjecture.
Supported partially by NSFC 10001035 and 10371055 |
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| Keywords: | plane graph circuit coloring |
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