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On 3-colorability of planar graphs without adjacent short cycles 被引量：4

On 3-colorability of planar graphs without adjacent short cycles
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摘要 A short cycle means a cycle of length at most 7.In this paper,we prove that planar graphs without adjacent short cycles are 3-colorable.This improves a result of Borodin et al.(2005). A short cycle means a cycle of length at most 7.In this paper,we prove that planar graphs without adjacent short cycles are 3-colorable.This improves a result of Borodin et al.(2005).
作者 WANG 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
出处 《Science China Mathematics》 SCIE 2010年第4期1129-1132,共4页 中国科学：数学（英文版）
基金 supported by the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6090699) National Natural Science Foundation of China (Grant No.10971198)
关键词 PLANAR GRAPH COLORING EXTENSION CYCLE planar graph coloring extension cycle
分类号 O157.5 [理学—基础数学]
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参考文献9

  • 1Daniel P. Sanders,Yue Zhao.A note on the three color problem[J]. Graphs and Combinatorics . 1995 (1)
  • 2Abbott,H. L.,Zhou,B.On small faces in 4-critical graphs. Ars Combinatoria . 1991
  • 3J. A. Bondy,,U. S. R. Murty.Graph Theory. . 2008
  • 4Borodin O V.Stmctural properties of plane graphs without adjacent triangles and application to 3-colorings. Journal of Graph Theory . 1996
  • 5Borodin,O. V.,Glebov,A. N.,Raspaud,A.,Salavatipour,M. R.Planar graphs without cycles of length from 4 to 7 are 3-colorable. Journal of Combinatorial Theory Series B . 2005
  • 6Gr?tzsch,H.Ein Drefarbensatz fur dreikreisfreie Netze auf der Kugel. Wiss Z Martin-Luther-Univ Halle-Wittenberg, Mat-Natur Reche . 1959
  • 7Jensen T R,Toft B.Graph Coloring Problems. . 1995
  • 8Sanders,D. P.,Zhao,Y.A note on the three coloring problem. Graphs and Combinatorics . 1995
  • 9Steinberg R.The state of the three color problem. Annals of Discrete Mathematics . 1993

同被引文献14

  • 1Dong Wei,Xu BaoGang,Zhang XiaoYan.Improved bounds on linear coloring of plane graphs[J].Science China Mathematics,2010,53(7):1891-1898. 被引量：4
  • 2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
  • 3王维凡,陈敏.不含4，6，8-圈的平面图是3-可染的[J].中国科学（A辑）,2007,37(8):982-992. 被引量：4
  • 4Montassier M, Raspaud A, Wang F W. A relaxation of Havel 's 3-color problem [J]. Information Processing Letters, 2008,107:107-109.
  • 5Borodin 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.
  • 6Borodin 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.
  • 7Borodin 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.
  • 8Borodin 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.
  • 9Luo 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.
  • 10许怡安,张晓岩.环面图上的一个Lebesgue型定理及其在线性染色中的应用[J].中国科学：数学,2011,41(5):477-484. 被引量：3

引证文献4

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Science China Mathematics
2010年 第4期

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