Skip to main content
SpringerLink
Log in

An Algebraic Characterization of Rainbow Connectivity

  • Conference paper
Computer Algebra in Scientific Computing (CASC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

Included in the following conference series:

  • 873 Accesses

Abstract

The use of algebraic techniques to solve combinatorial problems is studied in this paper. We formulate the rainbow connectivity problem as a system of polynomial equations. We first consider the case of two colors for which the problem is known to be hard and we then extend the approach to the general case. We also present a formulation of the rainbow connectivity problem as an ideal membership 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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N.: Combinatorial Nullstellensatz. Combinatorics, Probability and Computing 8(1&2), 7–29 (1999)

    MathSciNet  MATH  Google Scholar 

  2. Lovász, L.: Stable sets and polynomials. Discrete Mathematics 124(1-3), 137–153 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. De Loera, J.: Gröbner bases and graph colorings. Beiträge Algebra Geom. 36(1), 89–96 (1995)

    MATH  Google Scholar 

  4. De Loera, J., Lee, J., Malkin, P., Margulies, S.: Hilbert’s Nullstellensatz and an algorithm for proving combinatorial infeasibility. In: ISSAC 2008: Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation, pp. 197–206. ACM (2008)

    Google Scholar 

  5. Margulies, S.: Computer algebra, combinatorics, and complexity: Hilberts Nullstellensatz and NP-complete problems. PhD thesis, University of California (2008)

    Google Scholar 

  6. Bayer, D.: The division algorithm and the Hilbert scheme. PhD thesis, Harvard University (1982)

    Google Scholar 

  7. Cox, D.A., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms, 3rd edn. Undergraduate Texts in Mathematics. Springer (2007)

    Google Scholar 

  8. Kollár, J.: Sharp effective Nullstellensatz. American Mathematical Society 1(4) (1988)

    Google Scholar 

  9. Brownawell, W.: Bounds for the degrees in the Nullstellensatz. The Annals of Mathematics 126(3), 577–591 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  10. Loera, J., Lee, J., Margulies, S., Onn, S.: Expressing combinatorial problems by systems of polynomial equations and hilberts nullstellensatz. Combinatorics, Probability and Computing 18(04), 551–582 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chartrand, G., Johns, G., McKeon, K., Zhang, P.: Rainbow connection in graphs. Math. Bohem 133(1), 85–98 (2008)

    MathSciNet  MATH  Google Scholar 

  12. Alon, N., Tarsi, M.: A note on graph colorings and graph polynomials. Journal of Combinatorial Theory Series B 70, 197–201 (1997)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, 560012, India

    Prabhanjan Ananth & Ambedkar Dukkipati

Authors
  1. Prabhanjan Ananth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ambedkar Dukkipati
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ananth, P., Dukkipati, A. (2012). An Algebraic Characterization of Rainbow Connectivity. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32973-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation