SpringerLink
Log in

List Edge Coloring of Outer-1-planar Graphs

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number Χ′l(G) of any outer-1-planar graph G with maximum degree Δ(G) ≥ 5 is exactly its maximum degree. In this paper, we prove Χ′l(G) = Δ(G) for outer-1-planar graphs G with Δ(G) = 4 and with the crossing distance being at least 3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alon, N. Combinatorial Nullstellensatz. Combin. Probab. Comput., 8: 7–29 (1999)

    Article  MathSciNet  Google Scholar 

  2. Alon, N., Nathanson, M.B., Ruzsa, I.Z. The polynomial method and restricted sums of congruence classes. J. Number Theory, 56: 404–417 (1996)

    Article  MathSciNet  Google Scholar 

  3. Borodin, O.V., Kostochka, A.V., Woodall, D.R. List edge and list total colourings of multigraphs. J. Combin. Theory Ser. B, 71: 184–204 (1997)

    Article  MathSciNet  Google Scholar 

  4. Eggleton, R.B. Rectilinear drawings of graphs. Utilitas Math., 29: 149–172 (1986)

    MathSciNet  MATH  Google Scholar 

  5. Hetherington, T.J., Woodall, D.R. Edge and total choosability of near-outerplanar graphs. Electron. J. Combin., 13 (2006) #R98

    Article  MathSciNet  Google Scholar 

  6. Jensen, T.R., Toft, B. Graph Coloring Problems. Wiley-Interscience, New York, 1995

    MATH  Google Scholar 

  7. Juvan, M., Mohar, B., Thomas, R. List edge-colorings of series-parallel graphs. Electron. J. Combin., 6 (1999) #R42

    Article  MathSciNet  Google Scholar 

  8. Kfal, D., Stacho, L. Coloring plane graphs with independent crossings. J. Graph Theory, 64(3): 184–205 (2010)

    Article  MathSciNet  Google Scholar 

  9. Lewis, R.M.R. A Guide to Graph Colouring: Algorithms and Applications. Springer International Publishing, Switzerland, 2015

    Google Scholar 

  10. Tian, J., Zhang, X. Pseudo-outerplanar graphs and chromatic conjectures, Ars Combin., 114: 353–361 (2014)

    MathSciNet  MATH  Google Scholar 

  11. Wang, W., Lih, K.-W. Choosability, edge-choosability and total choosability of outerplane graphs. European J. Combin., 22: 71–78 (2001)

    Article  MathSciNet  Google Scholar 

  12. Wang, W., Zhang, K. A-Matchings and edge-face chromatic numbers. Acta Math. Appl. Sinica, 22: 236–242 (1999)

    MathSciNet  MATH  Google Scholar 

  13. Zhang, X. List total coloring of pseodo-outerplanar graphs. Discrete Math., 313: 2297–2306 (2013)

    Article  MathSciNet  Google Scholar 

  14. Zhang, X., Liu, C., Wu, J.L. Edge covering pseudo-outerplanar graphs with forests. Discrete Math., 312: 2788–2799 (2012)

    Article  MathSciNet  Google Scholar 

  15. Zhang, X. Total coloring of outer-1-planar graphs with near-independent crossings. J. Comb. Optim., 34(3): 661–675 (2017)

    Article  MathSciNet  Google Scholar 

  16. Zhang, X. The edge chromatic number of outer-l-planar graphs. Discrete Math., 339: 1393–1399 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The author thanks an anonymous reviewer who gave very detailed suggestions on the writing of Section 4.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, **dian University, **’an, 710071, China

    **n Zhang

Authors
  1. **n Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to **n Zhang.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 11871055, 11301410) and the Youth Talent Support Plan of **’an Association for Science and Technology, China (2018-6).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X. List Edge Coloring of Outer-1-planar Graphs. Acta Math. Appl. Sin. Engl. Ser. 36, 737–752 (2020). https://doi.org/10.1007/s10255-020-0940-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-020-0940-5

Keywords

2000 MR Subject Classification

Search

Navigation