Geodesic
Planar graphs without 4-, 5- and 8-cycles are 3-colorable
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 4, pp. 775-789.

Voir la notice de l'article provenant de la source Library of Science

In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.
Keywords: 3-coloring, planar graph, discharging 
@article{DMGT_2011_31_4_a10,
     author = {Mondal, Sakib},
     title = {Planar graphs without 4-, 5- and 8-cycles are 3-colorable},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {775--789},
     publisher = {mathdoc},
     volume = {31},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2011_31_4_a10/}
}
TY  - JOUR
AU  - Mondal, Sakib
TI  - Planar graphs without 4-, 5- and 8-cycles are 3-colorable
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2011
SP  - 775
EP  - 789
VL  - 31
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2011_31_4_a10/
LA  - en
ID  - DMGT_2011_31_4_a10
ER  - 
%0 Journal Article
%A Mondal, Sakib
%T Planar graphs without 4-, 5- and 8-cycles are 3-colorable
%J Discussiones Mathematicae. Graph Theory
%D 2011
%P 775-789
%V 31
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2011_31_4_a10/
%G en
%F DMGT_2011_31_4_a10
Mondal, Sakib. Planar graphs without 4-, 5- and 8-cycles are 3-colorable. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 4, pp. 775-789. http://geodesic.mathdoc.fr/item/DMGT_2011_31_4_a10/

[1] H.L. Abbott and B. Zhou, On small faces in 4-critical graphs, Ars Combin. 32 (1991) 203-207.

[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)21:2183::AID-JGT7>3.0.CO;2-N

[3] O.V. Borodin, To the paper: 'On small faces in 4-critical graphs', Ars Combin. 43 (1996) 191-192.

[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.

[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.

[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.

[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.

[12] R. Steinberg, The state of the three color problem, in: Ouo Vadis, Graph Theory? 55 (1993) 211-248.

[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.