论文信息 - Planar graphs without chordal 6-cycles are 4-choosable

Planar graphs without chordal 6-cycles are 4-choosable

Abstract A graph G is k -choosable if it can be colored whenever every vertex has a list of at least k available colors. In this paper, we prove that every planar graph without chordal 6-cycles is 4-choosable. This extends a known result that every planar graph without 6-cycles is 4-choosable.

Wei-Fan Wang | Jian-Liang Wu | Danjun Huang | Daiqiang Hu

[1] Baogang Xu,et al. The 4-Choosability of Plane Graphs without 4-Cycles' , 1999, J. Comb. Theory, Ser. B.

[2] J. A. Bondy,et al. Graph Theory with Applications , 1978 .

[3] Ko-Wei Lih,et al. Choosability and Edge Choosability of Planar Graphs without Intersecting Triangles , 2002, SIAM J. Discret. Math..

[4] Noga Alon,et al. Colorings and orientations of graphs , 1992, Comb..

[5] Wei-Fan Wang,et al. Vertex arboricity of planar graphs without chordal 6-cycles , 2013, Int. J. Comput. Math..

[6] Bojan Mohar,et al. Planar Graphs Without Cycles of Specific Lengths , 2002, Eur. J. Comb..

[7] Ko-Wei Lih,et al. Choosability and edge choosability of planar graphs without five cycles , 2002, Appl. Math. Lett..

[8] Babak Farzad. Planar Graphs without 7-Cycles Are 4-Choosable , 2009, SIAM J. Discret. Math..

[9] Carsten Thomassen,et al. Every Planar Graph Is 5-Choosable , 1994, J. Comb. Theory, Ser. B.

[10] Margit Voigt,et al. List colourings of planar graphs , 2006, Discret. Math..

[11] Ko-Wei Lih,et al. The 4-choosability of planar graphs without 6-cycles , 2001, Australas. J Comb..

[12] Margit Voigt,et al. A not 3-choosable planar graph without 3-cycles , 1995, Discret. Math..

[13] Baogang Xu,et al. On Structure of Some Plane Graphs with Application to Choosability , 2001, J. Comb. Theory B.