Skip to main content
SpringerLink
Log in

Free Choosability of Outerplanar Graphs

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

A graph G is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex \(u\ne v\), the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition for a cycle to be free (a, b)-choosable is given. As a corollary, we obtain almost optimal results about the free (a, b)-choosability of outerplanar graphs.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Alon, N., Tuza, Zs, Voigt, M.: Choosability and fractional chromatic number. Discret. Math. 165(166), 31–38 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aubry, Y., Godin, J.-C., Togni, O.: Every triangle-free induced subgraph of the triangular lattice is \((5m,2m)\)-choosable. Discret. Appl. Math. 166, 51–58 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bondy, J.A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics, vol. 244. Springer, New York (2008)

    MATH  Google Scholar 

  4. Erdős, P., Rubin, A.L., Taylor, H.: Choosability in graphs. In: Proceedings of the West-Coast Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium XXVI, pp. 125–157 (1979)

  5. Godin, J.-C.: Coloration et choisissabilité des graphes et applications. PhD Thesis (in french), Université du Sud Toulon-Var, France (2009)

  6. Gutner, S., Tarsi, M.: Some results on (a:b)-choosability. Discret. Math. 309, 2260–2270 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li, N., Meng, X., Liu, H.: Free Choosability of Outerplanar Graphs. In: Green Communications and Networks. Lecture Notes in Electrical Engineering, vol. 113, pp. 253–256 (2012)

  8. Tuza, Zs, Voigt, M.: Every 2-choosable graph is (2m, m)-choosable. J. Graph Theory 22, 245–252 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Voigt, M.: Choosability of planar graphs. Discret. Math. 150, 457–460 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Voigt, M.: On list Colourings and Choosability of Graphs. Abilitationsschrift, TU Ilmenau (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Mathématiques de Toulon, Université de Toulon, La Garde, France

    Yves Aubry & Jean-Christophe Godin

  2. Institut de Mathématiques de Marseille, Marseille, France

    Yves Aubry & Jean-Christophe Godin

  3. LE2I UMR 6306, CNRS, Arts et Métiers, Université Bourgogne Franche-Comté, DIJON, France

    Olivier Togni

Authors
  1. Yves Aubry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Christophe Godin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Olivier Togni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olivier Togni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aubry, Y., Godin, JC. & Togni, O. Free Choosability of Outerplanar Graphs. Graphs and Combinatorics 32, 851–859 (2016). https://doi.org/10.1007/s00373-015-1625-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-015-1625-3

Keywords

Mathematics Subject Classification

Search

Navigation