Skip to main content
SpringerLink
Log in
Book cover

International Conference on Algorithms and Complexity

CIAC 2015: Algorithms and Complexity pp 313–324Cite as

Deciding the On-line Chromatic Number of a Graph with Pre-coloring Is PSPACE-Complete

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9079))

Abstract

In an on-line coloring, the vertices of a graph are revealed one by one. An algorithm assigns a color to each vertex after it is revealed. When a vertex is revealed, it is also revealed which of the previous vertices it is adjacent to. The on-line chromatic number of a graph, \(G\), is the smallest number of colors an algorithm will need when on-line-coloring \(G\). The algorithm may know \(G\), but not the order in which the vertices are revealed. The problem of determining if the on-line chromatic number of a graph is less than or equal to \(k\), given a pre-coloring, is shown to be PSPACE-complete.

C. Kudahl—Supported in part by the Villum Foundation and the Danish Council for Independent Research, Natural Sciences.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bodlaender, H.L.: On the complexity of some coloring games. Internat. J. Found. Comput. Sci. 2, 133–147 (1989)

    Article  MathSciNet  Google Scholar 

  2. Gyarfas, A., Lehel, J.: First fit and on-line chromatic number of families of graphs. Ars Combinatorica 29C, 168–176 (1990)

    MATH  MathSciNet  Google Scholar 

  3. Gyarfas, A., Kiraly, Z., Lehel, J.: On-line competitive coloring algorithms. Tech. rep., Mathematical Institute of Eotvos Lorand University (1997). http://www.cs.elte.hu/tr97

  4. Kratochv, J.: Precoloring extension with fixed color bound. Acta Mathematica Universitatis Comenianae 62(2), 139–153 (1993). http://eudml.org/doc/118661

    MathSciNet  Google Scholar 

  5. Krawczyk, T., Walczak, B.: Coloring relatives of interval overlap graphs via on-line games. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 738–750. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  6. Kudahl, C.: On-line Graph Coloring. Master’s thesis, University of Southern Denmark (2013)

    Google Scholar 

  7. Kudahl, C.: Deciding the on-line chromatic number of a graph with pre-coloring is pspace-complete. CoRR abs/1406.1623 (2014). http://arxiv.org/abs/1406.1623

  8. Lehel, A.G.J., Kiraly, Z.: On-line graph coloring and finite basis problems. Combinatorics: Paul Erdos is Eighty, vol. 1, 207–214 (1993)

    Google Scholar 

  9. Marx, D.: Precoloring extension on unit interval graphs. Discrete Applied Mathematics 154(6), 995–1002 (2006). http://www.sciencedirect.com/science/article/pii/S0166218X05003392

    Article  MATH  MathSciNet  Google Scholar 

  10. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  11. Stockmeyer, L.J.: The polynomial-time hierarchy. Theoretical Computer Science 3(1), 1–22 (1976)

    Article  MathSciNet  Google Scholar 

  12. Tuza, Z.: Graph colorings with local constraints - a survey. Math. Graph Theory 17, 161–228 (1997)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Christian Kudahl

Authors
  1. Christian Kudahl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Kudahl .

Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    Vangelis Th. Paschos

  2. Inst. of Theoretical Computer Science, ETH Zürich, Zürich, Switzerland

    Peter Widmayer

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kudahl, C. (2015). Deciding the On-line Chromatic Number of a Graph with Pre-coloring Is PSPACE-Complete. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-18173-8_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18172-1

  • Online ISBN: 978-3-319-18173-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation