Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2002: Graph-Theoretic Concepts in Computer Science pp 138–149Cite as

A New 3-Color Criterion for Planar Graphs

Extended Abstract

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

Abstract

We present a new general 3-color criterion for planar graphs. Applying this criterion we characterize a broad class of 3-colorable planar graphs and provide a corresponding linear time 3-coloring algorithm. We also characterize fully infinite 3-colorable planar triangulations.

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. M. R. Garey, D. S. Johnson, and L. Stockmeyer, Some simplified NP-complete graph problems, Theoret. Comput. Sci., 1 (1976), pp. 237–267.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. J. Heawood, On the four-color map theorem, Quart. J. Pure Math. 29 (1898) 270–285

    MATH  Google Scholar 

  3. O. Ore, The Four-Color Problem, Academic Press, New York, Chapter 13 (1967).

    MATH  Google Scholar 

  4. R. Steinberg, The state of the three color problem [in:], Quo Vadis, Graph Theory? Annals of Discrete Mathematics, 55 (1993) 211–248

    Article  MathSciNet  Google Scholar 

  5. H. Król, On a sufficient and necessary condition of 3-colorableness for the planar graphs. I, Prace Naukowe Inst. Mat. i Fiz. Teoret. P. Wr., Seria Studia i Materialy, No. 6 Grafy i hypergrafy, (1972) 37–40

    Google Scholar 

  6. H. Król, On a sufficient and necessary condition of 3-colorableness for the planar graphs. II, Prace Naukowe Inst. Mat. i Fiz. Teoret. P. Wr., Seria Studia i Materialy, No. 9 Grafy i hypergrafy, (1973) 49–54

    Google Scholar 

  7. N. I. Martinov, 3-colorable planar graphs, Serdica, 3, (1977) 11–16

    MATH  MathSciNet  Google Scholar 

  8. M. Chrobak, D. Eppstein, Planar orientations with low out-degree and compactions of adjacency matrices Theoretical Computer Science, 86, (1991) 243–266

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Krzysztof Diks, Lukasz Kowalik & Maciej Kurowski

Authors
  1. Krzysztof Diks
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lukasz Kowalik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maciej Kurowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Diks, K., Kowalik, L., Kurowski, M. (2002). A New 3-Color Criterion for Planar Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-36379-3_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation