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Journal of Combinatorial Optimization

, Volume 32, Issue 1, pp 188–197 | Cite as

List edge and list total coloring of planar graphs with maximum degree 8

  • Huijuan WangEmail author
  • Bin Liu
  • Xin Zhang
  • Lidong Wu
  • Weili Wu
  • Hongwei Gao
Article

Abstract

Let \(G\) be a planar graph with maximum degree \(\varDelta \ge 8\) and without chordal 5-cycles. Then \(\chi '_{l}(G)=\varDelta \) and \(\chi ''_{l}(G)=\varDelta +1\).

Keywords

Choosability Planar graph List edge coloring  List total coloring 

Notes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 11201440, 11271006, 11301410, 11401386, 71171120, the Projects of International (Regional) Cooperation and Exchanges of NSFC (71411130215), the Specialized Research Fund for the Doctoral Program of Higher Education (20133706110002), the Shandong Provincial Natural Science Foundation of China under Grant ZR2014AQ001, the Natural Science Basic Research Plan in Shanxi Province of China under Grant 2013JQ1002, and the Scientific Research Foundation for the Excellent Young and Middle-Aged Scientists of Shandong Province of China under Grant BS2013-DX002.

References

  1. Angelini P, Frati F (2012) Acyclically 3-colorable planar graphs. J Comb Optim 24:116–130MathSciNetCrossRefzbMATHGoogle Scholar
  2. Borodin OV, Kostochka AV, Woodall DR (1997) List edge and list total colourings of multigraphs. J Comb Theory Ser B 71:184–204MathSciNetCrossRefzbMATHGoogle Scholar
  3. Du HW, Jia XH, Li DY, Wu WL (2004) Coloring of double disk graphs. J Global Optim 28:115–119MathSciNetCrossRefzbMATHGoogle Scholar
  4. Garg N, Papatriantafilou M, Tsigas P (1996) Distributed list coloring: how to dynamically allocate frequencies to mobile base stations. In: Eighth IEEE symposium on parallel and distributed processing, pp 18–25. doi: 10.1109/SPDP.1996.570312
  5. Hägkvist R, Chetwynd A (1992) Some upper bounds on the total and list chromatic numbers of multigraphs. J Graph Theory 16:503–516MathSciNetCrossRefzbMATHGoogle Scholar
  6. Hou JF, Liu GZ, Cai JS (2006) List edge and list total colorings of planar graphs without 4-cycles. Theor Comput Sci 369:250–255MathSciNetCrossRefzbMATHGoogle Scholar
  7. Jensen T, Toft B (1995) Graph coloring problems. Wiley-Interscience, New YorkzbMATHGoogle Scholar
  8. Li XW, Mak-Hau V, Zhou SM (2013) The \(L(2,1)\)-labelling problem for cubic Cayley graphs on dihedral groups. J Comb Optim 25:716–736MathSciNetCrossRefzbMATHGoogle Scholar
  9. Li R, Xu BG (2011) Edge choosability and total choosability of planar graphs with no 3-cycles adjacent 4-cycles. Discret Math 311:2158–2163MathSciNetCrossRefzbMATHGoogle Scholar
  10. Liu B, Hou JF, Wu JL, Liu GZ (2009) Total colorings and list total colorings of planar graphs without intersecting 4-cycles. Discret Math 309:6035–6043MathSciNetCrossRefzbMATHGoogle Scholar
  11. Wang HJ, Wu LD, Wu WL, Wu JL (2014) Minimum number of disjoint linear forests covering a planar graph. J Comb Optim 28:274–287MathSciNetCrossRefzbMATHGoogle Scholar
  12. Wang HJ, Wu LD, Zhang X, Wu WL, Liu B (2014) A note on the minimum number of choosability of planar graphs. J Comb Optim doi: 10.1007/s10878-014-9805-2
  13. Wang HJ, Wu LD, Wu WL, Pardalos PM, Wu JL (2014) Minimum total coloring of planar graph. J Global Optim 60:777–791MathSciNetCrossRefzbMATHGoogle Scholar
  14. Wang W, Liu X (2005) List coloring based channel allocation for open-spectrum wireless networks. In: IEEE 62nd vehicular technology conference (VTC 2005-Fall) (1):690–694, doi: 10.1109/VETECF.2005.1558001

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Huijuan Wang
    • 1
    Email author
  • Bin Liu
    • 2
  • Xin Zhang
    • 3
  • Lidong Wu
    • 4
  • Weili Wu
    • 5
    • 6
  • Hongwei Gao
    • 1
  1. 1.College of MathematicsQingdao UniversityQingdaoChina
  2. 2.Department of MathematicsOcean University of ChinaQingdaoChina
  3. 3.School of Mathematics and StatisticsXidian UniversityXi’anChina
  4. 4.Department of Computer ScienceUniversity of Texas at TylerTylerUSA
  5. 5.College of Computer Science and TechnologyTaiYuan University of TechnologyTaiyuanChina
  6. 6.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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