A Important Property on Planar Graph

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Abstract:

In 1994, C.Thomassen proved that every planar graph is (namely ). In 1993, M.Voigt shown that there are planar graphs which are not . But no one know whether every planar graph is . In this paper, we give a important property on planar graph that “Every planar graph is ” and “Every planar graph is free ” are equivalent.

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245-248

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February 2011

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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[1] V.G. Vizing: Coloring the vertices of a graph in prescribed colors(in Russian). Diskret. Anal. Vol. 29(1976).

Google Scholar

[2] P. Erdos, A.L. Rubin and H. Taylor: Choosability in graphs, Congr. Numer. Vol. 26(1979).

Google Scholar

[3] C. Thomassen: Every planar graph is 5-choosable, J. Combin. Theory Ser. B Vol. 62(1994).

Google Scholar

[4] M. Voigt: List colourings of planar graphs, Discrete Math. Vol. 120(1993).

Google Scholar

[5] S. Gutner: The complexity of planar graph choosability, Discrete Math. Vol. 159(1996).

DOI: 10.1016/0012-365x(95)00104-5

Google Scholar

[6] M. Mirzakhani: A small non-4-choosable planar graph, Bull Inst. Combin. Appl. Vol. 17(1996).

Google Scholar

[7] R. · Skrekovski: List improper colourings of planar graphs, Combin. Prob. Comput. Vol. 8(1999).

Google Scholar

[8] N. Eaton and T. Hull: Defective list colorings of planar graphs, Bull Inst. Combin. Appl. Vol. 25(1999).

Google Scholar

[9] M. Voigt: Choosability of planar graphs, Discrete M ath. Vol. 150(1996).

Google Scholar

[10] D.R. Woodall: Defective choosability results for outerplanar and related graphs, Discrete Math. Vol. 258(2002).

DOI: 10.1016/s0012-365x(02)00300-x

Google Scholar

[11] D.R. Woodall: List colourings of graphs, Survey in combinatorics, 2001, London Math. Soc. Lecture Note Series 288, Cambridge University Press(2001).

Google Scholar