Discussiones Mathematicae Graph Theory 31(3) (2011)
441-459
doi: 10.7151/dmgt.1557
Douglas R. Woodall
School of Mathematical Sciences
University of Nottingham
Nottingham NG7 2RD, UK
e-mail: douglas.woodall@nottingham.ac.uk
Keywords: list coloring, defective coloring, minor-free graph.
2010 Mathematics Subject Classification: 05C15.
[1] | D. Archdeacon, A note on defective colorings of graphs in surfaces, J. Graph Theory 11 (1987) 517-519, doi: 10.1002/jgt.3190110408. |
[2] | L.J. Cowen, R.H. Cowen and D.R. Woodall, Defective colorings of graphs in surfaces: partitions into subgraphs of bounded valency, J. Graph Theory 10 (1986) 187-195, doi: 10.1002/jgt.3190100207. |
[3] | L. Cowen, W. Goddard and C.E. Jesurum, Defective coloring revisited, J. Graph Theory 24 (1997) 205-219, doi: 10.1002/(SICI)1097-0118(199703)24:3<205::AID-JGT2>3.0.CO;2-T. |
[4] | W. Cushing and H.A. Kierstead, Planar graphs are 1-relaxed, 4-choosable, European J. Combin. 31 (2010) 1385-1397, doi: 10.1016/j.ejc.2009.11.013. |
[5] | G.A. Dirac, A property of 4-chromatic graphs and some remarks on critical graphs, J. London Math. Soc. 27 (1952) 85-92, doi: 10.1112/jlms/s1-27.1.85. |
[6] | N. Eaton and T. Hull, Defective list colorings of planar graphs, Bull Inst. Combin. Appl. 25 (1999) 79-87. |
[7] | S. Gutner, The complexity of planar graph choosability, Discrete Math. 159 (1996) 119-130, doi: 10.1016/0012-365X(95)00104-5. |
[8] | W. He, W. Miao and Y. Shen, Another proof of the 5-choosability of K_{5}-minor-free graphs, Discrete Math. 308 (2008) 4024-4026, doi: 10.1016/j.disc.2007.07.089. |
[9] | M. Mirzakhani, A small non-4-choosable planar graph, Bull Inst. Combin. Appl. 17 (1996) 15-18. |
[10] | N. Robertson, P.D. Seymour and R. Thomas, Hadwiger's conjecture for K_{6}-free graphs, Combinatorica 13 (1993) 279-361, doi: 10.1007/BF01202354. |
[11] | R. Skrekovski, Choosability of K_{5}-minor-free graphs, Discrete Math. 190 (1998) 223-226, doi: 10.1016/S0012-365X(98)00158-7. |
[12] | R. Skrekovski, List improper colourings of planar graphs, Combin. Probab. Comput. 8 (1999) 293-299, doi: 10.1017/S0963548399003752. |
[13] | C. Thomassen, Every planar graph is 5-choosable, J. Combin. Theory (B) 62 (1994) 180-181, doi: 10.1006/jctb.1994.1062. |
[14] | M. Voigt, List colourings of planar graphs, Discrete Math. 120 (1993) 215-219, doi: 10.1016/0012-365X(93)90579-I. |
[15] | K. Wagner, Über eine Eigenschaft der ebenen Komplexe, Math. Ann. 114 (1937) 570-590, doi: 10.1007/BF01594196. |
[16] | D.R. Woodall, Improper colourings of graphs, in: R. Nelson and R.J. Wilson (eds.), Graph Colourings, Pitman Research Notes in Math. 218 (Longman, Harlow, Essex, 1990) 45-63. |
[17] | D.R. Woodall, List Colourings of Graphs, in: J.W.P. Hirschfeld (ed), Surveys in Combinatorics, 2001, London Math. Soc. Lecture Note Series 288 (Cambridge University Press, 2001) 269-301. |
Received 10 March 2010
Accepted 4 May 2010