Planar graphs without 4-, 5- and 8-cycles are 3-colorable
Discussiones Mathematicae Graph Theory (2011)
- Volume: 31, Issue: 4, page 775-789
- ISSN: 2083-5892
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topSakib A. Mondal. "Planar graphs without 4-, 5- and 8-cycles are 3-colorable." Discussiones Mathematicae Graph Theory 31.4 (2011): 775-789. <http://eudml.org/doc/270962>.
@article{SakibA2011,
abstract = {In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.},
author = {Sakib A. Mondal},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {3-coloring; planar graph; discharging},
language = {eng},
number = {4},
pages = {775-789},
title = {Planar graphs without 4-, 5- and 8-cycles are 3-colorable},
url = {http://eudml.org/doc/270962},
volume = {31},
year = {2011},
}
TY - JOUR
AU - Sakib A. Mondal
TI - Planar graphs without 4-, 5- and 8-cycles are 3-colorable
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 4
SP - 775
EP - 789
AB - In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.
LA - eng
KW - 3-coloring; planar graph; discharging
UR - http://eudml.org/doc/270962
ER -
References
top- [1] H.L. Abbott and B. Zhou, On small faces in 4-critical graphs, Ars Combin. 32 (1991) 203-207. Zbl0755.05062
- [2] O.V. Borodin, Structural properties of plane graphs without adjacent triangles and an application to 3-colorings, J. Graph Theory 21 (1996 ) 183-186, doi: 10.1002/(SICI)1097-0118(199602)21:2<183::AID-JGT7>3.0.CO;2-N Zbl0838.05039
- [3] O.V. Borodin, To the paper: 'On small faces in 4-critical graphs', Ars Combin. 43 (1996) 191-192. Zbl0881.05037
- [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. Zbl1056.05052
- [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. Zbl1023.05046
- [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. Zbl1184.05024
- [8] M. Chen, A. Raspaud and W. Wang, Three-coloring planar graphs without short cycles, Information Processing Letters 101 (2007) 134-138, doi: 10.1016/j.ipl.2006.08.009. Zbl1185.05057
- [9] H. Grotsch, Ein Dreifarbensatz fur dreikreisfreie Netze auf der Kugel, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg, Mat.-Natur. Reihe 8 (1959) 102-120.
- [10] I. Havel, On a conjecture of Grünbaum, J. Combin. Theory (B) 7 (1969), 184-186, doi: 10.1016/S0021-9800(69)80054-2. Zbl0177.26805
- [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. Zbl0824.05023
- [12] R. Steinberg, The state of the three color problem, in: Ouo Vadis, Graph Theory? 55 (1993) 211-248. Zbl0791.05044
- [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. Zbl1144.05033
- [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. Zbl1185.05061
- [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. Zbl1122.05038
- [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. Zbl1070.05046
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