Skip to main content
SpringerLink
Log in

The Alcuin Number of a Graph

  • Conference paper
Book cover Algorithms - ESA 2008 (ESA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5193))

Included in the following conference series:

Abstract

We consider a planning problem that generalizes Alcuin’s river crossing problem (also known as: The wolf, goat, and cabbage puzzle) to scenarios with arbitrary conflict graphs. We derive a variety of combinatorial, structural, algorithmical, and complexity theoretical results around this problem.

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

Access this chapter

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 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 189.00
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ascher, M.: A river-crossing problem in cross-cultural perspective. Mathematics Magazine 63, 26–29 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bahls, P.: The wolf, the goat, and the cabbage: A modern twist on a classical problem. University of North Carolina, Asheville (unpublished manuscript, 2005)

    Google Scholar 

  3. Biggs, N.L.: The roots of combinatorics. Historia Mathematica 6, 109–136 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  4. Borndörfer, R., Grötschel, M., Löbel, A.: Alcuin’s transportation problems and integer programming. In: Charlemagne and his heritage. 1200 years of civilization and science in Europe, Brepols, Turnhout, vol. 2, pp. 379–409 (1998)

    Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  6. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)

    MATH  Google Scholar 

  7. Grötschel, M., Lovász, L., Schrijver, A.: Geometric algorithms and combinatorial optimization. Springer, New York (1988)

    MATH  Google Scholar 

  8. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. Journal of Computer and System Sciences 74, 335–349 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lampis, M., Mitsou, V.: The ferry cover problem. In: Crescenzi, P., Prencipe, G., Pucci, G. (eds.) FUN 2007. LNCS, vol. 4475, pp. 227–239. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Lovász, L., Plummer, M.D.: Matching Theory. Annals of Discrete Mathematics, vol. 29. North-Holland, Amsterdam (1986)

    MATH  Google Scholar 

  11. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, New York (2006)

    MATH  Google Scholar 

  12. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  13. Prisner, E.: Generalizing the wolf-goat-cabbage problem. Electronic Notes in Discrete Mathematics 27, 83 (2006)

    Article  Google Scholar 

  14. Schrijver, A.: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory, Series B 80, 346–355 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Péter Csorba, Cor A. J. Hurkens & Gerhard J. Woeginger

Authors
  1. Péter Csorba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cor A. J. Hurkens
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gerhard J. Woeginger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Dan Halperin Kurt Mehlhorn

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Csorba, P., Hurkens, C.A.J., Woeginger, G.J. (2008). The Alcuin Number of a Graph. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-87744-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87743-1

  • Online ISBN: 978-3-540-87744-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation