Skip to main content

A Guided Tour in Random Intersection Graphs

  • Conference paper
Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7966))

Included in the following conference series:

Abstract

Random graphs, introduced by P. Erdős and A. Rényi in 1959, still attract a huge amount of research in the communities of Theoretical Computer Science, Algorithms, Graph Theory, Discrete Mathematics and Statistical Physics. This continuing interest is due to the fact that, besides their mathematical beauty, such graphs are very important, since they can model interactions and faults in networks and also serve as typical inputs for an average case analysis of algorithms. The modeling effort concerning random graphs has to show a plethora of random graph models; some of them have quite elaborate definitions and are quite general, in the sense that they can simulate many other known distributions on graphs by carefully tuning their parameters.

This research was partially supported by the EU IP Project MULTIPLEX contract number 317532.

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

Access this chapter

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. Behrisch, M., Taraz, A., Ueckerdt, M.: Coloring random intersection graphs and complex networks. SIAM J. Discrete Math. 23, 288–299 (2008)

    Article  MathSciNet  Google Scholar 

  2. Cooper, C., Frieze, A.: The Cover Time of Sparse Random Graphs. In: Random Structures and Algorithms, vol. 30, pp. 1–16. John Wiley & Sons, Inc. (2007)

    Google Scholar 

  3. Efthymiou, C., Spirakis, P.G.: Sharp thresholds for Hamiltonicity in random intersection graphs. Theor. Comput. Sci. 411(40-42), 3714–3730 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fill, J.A., Sheinerman, E.R., Singer-Cohen, K.B.: Random intersection graphs when m = ω(n): an equivalence theorem relating the evolution of the G(n, m, p) and G(n, p) models. Random Struct. Algorithms 16(2), 156–176 (2000)

    Article  MATH  Google Scholar 

  5. Frieze, A.: On the Independence Number of Random Graphs. Disc. Math. 81, 171–175 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. Godehardt, E., Jaworski, J.: Two models of Random Intersection Graphs for Classification. In: Opitz, O., Schwaiger, M. (eds.). Studies in Classification, Data Analysis and Knowledge Organisation, pp. 67–82. Springer, Heidelberg (2002)

    Google Scholar 

  7. Karoński, M., Sheinerman, E.R., Singer-Cohen, K.B.: On Random Intersection Graphs: The Subgraph Problem. Combinatorics, Probability and Computing Journal 8, 131–159 (1999)

    Article  MATH  Google Scholar 

  8. Łuczak, T.: The chromatic number of random graphs. Combinatorica 11(1), 45–54 (2005)

    Google Scholar 

  9. Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Coloring Non-sparse Random Intersection Graphs. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 600–611. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Expander properties and the cover time of random intersection graphs. Theor. Comput. Sci. 410(50), 5261–5272 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Large independent sets in general random intersection graphs. Theor. Comput. Sci. 406, 215–224 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Maximum Cliques in Graphs with Small Intersection Number and Random Intersection Graphs. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 728–739. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: On the Independence Number and Hamiltonicity of Uniform Random Intersection Graphs. Theor. Comput. Sci. 412(48), 6750–6760 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Molloy, M., Reed, B.: Graph Colouring and the Probabilistic Method. Springer (2002)

    Google Scholar 

  15. Raptopoulos, C., Spirakis, P.G.: Simple and Efficient Greedy Algorithms for Hamilton Cycles in Random Intersection Graphs. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 493–504. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Rybarczyk, K.: Equivalence of a random intersection graph and G(n, p). Random Structures and Algorithms 38(1-2), 205–234 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shang, Y.: On the Isolated Vertices and Connectivity in Random Intersection Graphs. International Journal of Combinatorics 2011, Article ID 872703 (2011), doi:10.1155/2011/872703

    Google Scholar 

  18. Singer-Cohen, K.B.: Random Intersection Graphs. PhD thesis, John Hopkins University (1995)

    Google Scholar 

  19. Stark, D.: The vertex degree distribution of random intersection graphs. Random Structures & Algorithms 24(3), 249–258 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Spirakis, P.G., Nikoletseas, S., Raptopoulos, C. (2013). A Guided Tour in Random Intersection Graphs. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39212-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39211-5

  • Online ISBN: 978-3-642-39212-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics