SpringerLink
Log in

List Strong Edge-Colorings of Sparse Graphs

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

A strong edge-coloring of a graph \(G=(V,E)\) is a partition of its edge set E into induced matchings. In this paper, we will study the list version of strong edge-colorings of several classes of sparse graphs, including bipartite graphs and graphs with small edge weight, where the edge weight of a graph is defined by \(\max \{ d_G(u) + d_G(v)| uv \in E(G)\}\). We show that: (1) if G is a bipartite graph with bipartition (A, B) such that \(\Delta (A)=2\) and \(\Delta (B)=\Delta \ge 4\), then G has strong list-chromatic index at most \(3\Delta -3\); (2) every graph with edge weight at most 5 (resp. 6) has strong list-chromatic index at most 7 (resp. 11) and every planar graph with edge weight at most 6 has strong list-chromatic index at most 10; and (3) every graph with edge weight at most 7 has strong list-chromatic index at most 16.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Anderson, L.D.: The strong chromatic index of a cubic graph is at most 10. Discrete Math. 108, 231–252 (1992)

    Article  MathSciNet  Google Scholar 

  2. Brualdi, A.T., Quinn Massey, J.J.: Incidence and strong edge-colorings of graphs. Discrete Math. 122, 51–58 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, L., Huang, M., Yu, G., Zhou, X.: The strong edge-coloring for graphs with small edge weight. Discrete Math. 343(4), 111779 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, M., Hu, J., Yu, X., Zhou, S.: List strong edge-coloring of planar graphs with maximum degree 4. Discrete Math. 342, 1471–1480 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dai, T., Wang, G., Yang, D., Yu, G.: Strong list-chromatic index of subcubic graphs. Discrete Math. 341, 3434–3440 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Erdős, P., Nešetřil, J.: Irregularities of partitions. In: Halasz, G., Sòs, V.T. (Eds.) Problem, pp. 162–163 (1989)

  7. Fouquet, J.L., Jolivet, J.L.: Strong edge-colorings of graphs and applications to multi-\(k\)-gons. Ars Combin. 16A, 141–150 (1983)

    MathSciNet  MATH  Google Scholar 

  8. Hall, P.: On representatives of subsets. J. Lond. Math. Soc. 10(1), 26–30 (1935)

    Article  MathSciNet  MATH  Google Scholar 

  9. Horák, P., Qing, H., Trotter, W.T.: Induced matchings in cubic graphs. J. Graph Theory 17, 151–160 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Huang, M., Santana, M., Yu, G.: Strong chromatic index of graphs with maximum degree four. Electron. J. Combin. 25(3), 31 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  11. Huang, M., Yu, G., Zhou, X.: The strong chromatic index of \((3, \Delta )\)-bipartite graphs. Discrete Math. 340, 1143–1149 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kang, S., Park, B.: On incidence choosability of cubic graphs. Discrete Math. 342(6), 1828–1837 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ma, H., Miao, Z., Zhu, H., Zhang, J., Luo, R.: Strong list edge-coloring of subcubic graphs. Math. Probl. Eng. 316501, 6 (2013)

    MathSciNet  MATH  Google Scholar 

  14. Nakprasit, K.: A note on the strong chromatic index of bipartite graphs. Discrete Math. 308, 3726–3728 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu, J., Lin, W.: The strong chromati c index of a class of graphs. Discrete Math. 308, 6254–6261 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang, B., Chang, Y., Hu, J., Ma, M., Yang, D.: List strong edge-coloring of graphs with maximum degree 4. Discrete Math. 343(6), 111854 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhu, H., Miao, Z.: On strong list edge-coloring of subcubic graphs. Discrete Math. 333, 6–13 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, China

    Kecai Deng, Ningge Huang & Haiyang Zhang

  2. Department of Mathematics and Statistics, Wright State University, Dayton, OH, 45435, USA

    **angqian Zhou

Authors
  1. Kecai Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ningge Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haiyang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. **angqian Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us.

Corresponding author

Correspondence to Kecai Deng.

Ethics declarations

Conflict of interest

We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Human and animal rights

Additional declarations for articles in life science journals that report the results of studies involving humans and/or animals.

Additional information

Communicated by Wen Chean Teh.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The first author (Kecai Deng) is supported by NSFC (No. 11701195).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, K., Huang, N., Zhang, H. et al. List Strong Edge-Colorings of Sparse Graphs. Bull. Malays. Math. Sci. Soc. 46, 199 (2023). https://doi.org/10.1007/s40840-023-01594-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40840-023-01594-z

Keywords

Mathematics Subject Classification

Search

Navigation