Advertisement

Optimal channel assignment with list-edge coloring

  • Huijuan WangEmail author
  • Panos M. Pardalos
  • Bin Liu
Article
  • 39 Downloads

Abstract

Motivated from optimal channel assignment in optical networks, the list edge (and total) coloring are studied in this paper. In a special case of planar graphs, we determined the list edge (and total) coloring number.

Keywords

Choosability Planar graph Intersecting Chordal 

Notes

Funding

Funding was provided by National Natural Science Foundation of China (Grant Nos. 11501316, 11871442).

References

  1. Bessy S, Havet F (2013) Enumerating the edge-colourings and total colourings of a regular graph. J Comb Optim 25:523–535MathSciNetCrossRefzbMATHGoogle 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 Glob 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.  https://doi.org/10.1109/SPDP.1996.570312
  5. Gutner S (1996) The complexity of planar graph choosability. Discrete Math 159(1):119–130MathSciNetCrossRefzbMATHGoogle Scholar
  6. Gutner S, Tarsi M (2009) Some results on \((a, b)\)-choosability. Discrete Math 309(8):2260–2270MathSciNetCrossRefzbMATHGoogle Scholar
  7. Hägkvist R, Chetwynd A (1992) Some upper bounds on the total and list chromatic numbers of multigraphs. J Graph Theory 16:503–516MathSciNetCrossRefzbMATHGoogle Scholar
  8. 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
  9. Jensen T, Toft B (1995) Graph coloring problems. Wiley-Interscience, New YorkzbMATHGoogle Scholar
  10. Kowalik L, Socala A (2018) Tight lower bounds for list edge coloring. arXiv:1804.02537v1
  11. Li R, Xu BG (2011) Edge choosability and total choosability of planar graphs with no 3-cycles adjacent 4-cycles. Discrete Math 311:2158–2163MathSciNetCrossRefzbMATHGoogle Scholar
  12. Liu B, Hou JF, Wu JL, Liu GZ (2009) Total colorings and list total colorings of planar graphs without intersecting 4-cycles. Discrete Math 309:6035–6043MathSciNetCrossRefzbMATHGoogle Scholar
  13. Roberts FS (1991) T-colorings of a graphs:recent results and open problems. Discrete Math 93:229–245MathSciNetCrossRefGoogle Scholar
  14. Shi YS, Zhang YP, Zhang Z, Wu WL (2016) A greedy algorithm for the minimum 2-connected m-fold dominating set problem. J Comb Optim 31(1):136–151MathSciNetCrossRefzbMATHGoogle Scholar
  15. Shi YS, Zhang Z, Mo YC, Du DZ (2017) Approximation algorithm for minimum weight fault-tolerant virtual backbone in unit disk graphs. IEEE/ACM Trans Netw 25(2):925–933CrossRefGoogle Scholar
  16. Wang W, Liu X (2005) List coloring based channel allocation for open-spectrum wireless networks. IN: IEEE 62nd vehicular technology conference (VTC 2005-Fall), vol 1, pp 690–694Google Scholar
  17. Wang HJ, Wu LD, Wu WL, Pardalos PM, Wu JL (2014) Minimum total coloring of planar graph. J Glob Optim 60:777–791MathSciNetCrossRefzbMATHGoogle Scholar
  18. Wang HJ, Wu LD, Zhang X, Wu WL, Liu B (2016) A note on the minimum number of choosability of planar graphs. J Comb Optim 31:1013–1022MathSciNetCrossRefzbMATHGoogle Scholar
  19. Zhang Z, Zhou J, Tang SJ, Huang XH, Du DZ (2018) Computing minimum k-connected m-fold dominating set in general graphs. INFORMS J Comput 30(2):217–224MathSciNetCrossRefGoogle Scholar
  20. Zhou J, Zhang Z, Tang SJ, Huang XH, Mo YC, Du DZ (2017) Fault-tolerant virtual backbone in heterogeneous wireless sensor network. IEEE/ACM Trans Netw 25(6):3487–3499CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsQingdao UniversityQingdaoChina
  2. 2.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.School of Mathematical SciencesOcean University of ChinaQingdaoChina

Personalised recommendations