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2011 | 31 | 4 | 775-789

Tytuł artykułu

Planar graphs without 4-, 5- and 8-cycles are 3-colorable

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.

Słowa kluczowe

Wydawca

Rocznik

Tom

31

Numer

4

Strony

775-789

Daty

wydano
2011
otrzymano
2010-04-05
zaakceptowano
2010-11-26

Twórcy

  • Enterprise Analytics Group, India Science Lab, General Motors Global Research and Development, GM Technical Centre India Pvt Ltd, Creator Bldg., International Tech Park Ltd., Whitefield Road, Bangalore 560 066, India

Bibliografia

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  • [4] O.V. Borodin, A.N. Glebov, A. Raspaud and M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory (B) 93 (2005) 303-311, doi: 10.1016/j.jctb.2004.11.001.
  • [5] O.V. Borodin and A.N. Glebov, A sufficient condition for plane graphs to be 3-colorable, Diskret Analyz Issled. Oper. 10 (2004) 3-11.
  • [6] O.V. Borodin and A. Raspaud, A sufficient condition for planar graph to be 3-colorable, J. Combin. Theory (B) 88 (2003) 17-27, doi: 10.1016/S0095-8956(03)00025-X.
  • [7] O.V. Borodin, A.N. Glebov, M. Montassier and A. Raspaud, Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable, J. Combin. Theory (B) 99 (2009) 668-673, doi: 10.1016/j.jctb.2008.11.001.
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  • [11] D.P. Sanders and Y. Zhao, A note on the three color problem, Graphs and Combin. 11 (1995) 91-94, doi: 10.1007/BF01787424.
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  • [13] W. Wang. and M. Chen, Planar graphs without 4,6,8-cycles are 3-colorable, Science in China Series A: Mathematics (Science in China Press, co-published with Springer-Verlag GmbH) 50 (2007) 1552-1562.
  • [14] L. Xiaofang, M. Chen and W. Wang, On 3-colorable planar graphs without cycles of four lengths, Information Processing Letters 103 (2007) 150-156, doi: 10.1016/j.ipl.2007.03.007.
  • [15] B.Xu, A 3-color theorem on plane graph without 5-circuits, Acta Mathematica Sinica 23 (2007) 1059-1062, doi: 10.1007/s10114-005-0851-7.
  • [16] L. Zhang and B. Wu, A note on 3-choosability of planar graphs without certain cycles, Discrete Math. 297 (2005) 206-209, doi: 10.1016/j.disc.2005.05.001.

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