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平面图3-可着色的3个充分条件 被引量：3

Three Sufficient Conditions for Planar Graphs to be 3-Colorable
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摘要 平面图3-可着色是指可用3种颜色对该图的顶点进行着色,使得相邻的顶点着不同的颜色.研究了平面图在长度不大于6的圈或长度不大于7的圈之间满足一定条件下是3-可着色的. A planar graph is 3-colorable if its vertices can be colored with three colors, no two adjacent vertices coloring the same color. It has studied that planar graphs which can be 3-colorable provided that the cycles of length at most 6 or 7 which satisfy some conditions.
作者 彩春丽 谢德政
机构地区 重庆大学数学与统计学院
出处 《河南师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第6期4-6,28,共4页 Journal of Henan Normal University(Natural Science Edition)
基金 重庆市科委自然科学基金(CSTC 2007BB2123)
关键词 平面图 圈 距离 3-可着色 planar graphs cycles distance 3-colorable
分类号 O157.5 [理学—基础数学]
  • 相关文献

参考文献8

  • 1WANG YingQian 1,MAO XiangHua 1,LU HuaJing 2 & WANG WeiFan 1 1 College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua 321004,China,2 College of Basic Science,Ningbo Dahongying University,Ningbo 315175,China.On 3-colorability of planar graphs without adjacent short cycles[J].Science China Mathematics,2010,53(4):1129-1132. 被引量：4
  • 2Montassier M, Raspaud A, Wang F W. A relaxation of Havel 's 3-color problem [J]. Information Processing Letters, 2008,107:107-109.
  • 3Borodin O V, Montassier M, Raspaud A. Planar graphs without adjacent cycles of length at most seven are 3-colorable [J]. Discrete Mathematics, 2010,310 : 167-173.
  • 4Borodin O V, Glebov A N, Raspaud A. Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable [J]. Discrete Mathematics, 2010,310 : 2584-2594.
  • 5Borodin OV, Glebov A N, RasPaud A. Planar graphs without cycles of length from 4 to 7 are 3-colorable [J]. Journal of Combinatorial Theory, Series B,2005,93(2) :303-311.
  • 6Borodin O V, Gtebov A N, Montassier M. Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable [J]. Journal of Combinatorial Theory, Series B,2009,99:668-673.
  • 7Luo X F, Chen M, Wang W F. On 3-colorable planar graphs without cycles of four lengths [J]. Information Processing Letters,2007, 103 : 150-156.
  • 8鲁晓旭,许宝刚.关于平面图3-可着色的一个定理(英文)[J].南京师大学报（自然科学版）,2006,29(3):5-8. 被引量：4

二级参考文献17

  • 1Steinberg R. The state of the three color problem[J]. Ann Discrete Math, 1993,55:211 -248.
  • 2Borodin O V. Structural properties of plane graphs without adjacent triangles and an application to 3-colorings[ J ]. Journal of Graph Theory, 1996,21 (2) : 183 - 186.
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  • 6Borodin O V, Raspaud A. A sufficient condition for planar graphs to be 3-colorable[ J ]. Journal Combinatorial Theory Ser B,2003,88 ( 1 ) : 17 - 27.
  • 7Zhang L, Wu B. Three-choosable planar graphs without certain small cycles[J]. Graph Theory Notes of New York, 2004,46:27 - 30.
  • 8Bondy J A, Murty U S R. Graph Theory with Applications[M]. London: Macmillan Press Ltd, 1976.
  • 9Daniel P. Sanders,Yue Zhao.A note on the three color problem[J]. Graphs and Combinatorics . 1995 (1)
  • 10Abbott,H. L.,Zhou,B.On small faces in 4-critical graphs. Ars Combinatoria . 1991

共引文献6

同被引文献24

引证文献3

二级引证文献4

河南师范大学学报（自然科学版）
2011年 第6期

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