Discussiones Mathematicae Graph Theory 27(3) (2007)
425-455
doi: 10.7151/dmgt.1372
Douglas R. Woodall
School of Mathematical Sciences
University of Nottingham
Nottingham NG7 2RD, UK
e-mail: douglas.woodall@nottingham.ac.uk
Keywords: maximum average degree, planar graph, total choosability, list total colouring.
2000 Mathematics Subject Classification: Primary: 05C15; Secondary: 05C35.
[1] | N. Alon and M. Tarsi, Colorings and orientations of graphs, Combinatorica 12 (1992) 125-134, doi: 10.1007/BF01204715. |
[2] | O.V. Borodin, A.V. Kostochka and D.R. Woodall, List edge and list total colourings of multigraphs, J. Combin. Theory (B) 71 (1997) 184-204, doi: 10.1006/jctb.1997.1780. |
[3] | O.V. Borodin, A.V. Kostochka and D.R. Woodall, Total colourings of planar graphs with large girth, European J. Combin. 19 (1998) 19-24, doi: 10.1006/eujc.1997.0152. |
[4] | A. Chetwynd, Total colourings of graphs, in: R. Nelson and R.J. Wilson, eds, Graph Colourings (Milton Keynes, 1988), Pitman Res. Notes Math. Ser. 218 (Longman Sci. Tech., Harlow, 1990) 65-77. |
[5] | P. Erdös, A.L. Rubin and H. Taylor, Choosability in graphs, in: Proc. West Coast Conference on Combinatorics, Graph Theory and Computing, Arcata, 1979, Congr. Numer. 26 (1980) 125-157. |
[6] | M. Juvan, B. Mohar and R. Skrekovski, List total colourings of graphs, Combin. Probab. Comput. 7 (1998) 181-188, doi: 10.1017/S0963548397003210. |
[7] | L. Lovász, Three short proofs in graph theory, J. Combin. Theory (B) 19 (1975) 269-271, doi: 10.1016/0095-8956(75)90089-1. |
[8] | V.G. Vizing, Colouring the vertices of a graph in prescribed colours (in Russian), Metody Diskret. Analiz. 29 (1976) 3-10. |
[9] | W. Wang, Total chromatic number of planar graphs with maximum degree 10, J. Graph Theory 54 (2007) 91-102, doi: 10.1002/jgt.20195. |
[10] | D.R. Woodall, List colourings of graphs, in: J.W.P. Hirschfeld, ed., Surveys in Combinatorics, 2001, London Math. Soc. Lecture Note Ser. 288 (Cambridge Univ. Press, Cambridge, 2001) 269-301. |
Received 21 April 2006
Revised 6 July 2007
Accepted 6 July 2007