Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 453808, 9 pages
http://dx.doi.org/10.1155/2013/453808
Research Article

Decomposable Convexities in Graphs and Hypergraphs

Computer Science Department, Sapienza University of Rome, 00198 Rome, Italy

Received 4 October 2012; Accepted 23 October 2012

Academic Editors: E. Manstavicius and W. Menasco

Copyright © 2013 Francesco M. Malvestuto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Van de Vel, Theory of Convex Structures, North-Holland, Amsterdam, The Netherlands, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Duchet, “Discrete convexity: retractions, morphisms and the partition problem,” in Proceedings of the Conference on Graph Connections, pp. 1–16, Allied Publishers, 1998. View at Zentralblatt MATH · View at MathSciNet
  3. E. Sampathkumar, “Convex sets in a graph,” Indian Pure and Applied Mathematics, vol. 15, pp. 1065–1071, 1984. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Farber and R. E. Jamison, “Convexity in graphs and hyper graphs,” SIAM Journal on Algebraic and Discrete Methods, vol. 7, pp. 433–444, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. Duchet, “Convex sets in graphs, II. Minimal path convexity,” Journal of Combinatorial Theory B, vol. 44, no. 3, pp. 307–316, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. M. Changat and J. Mathew, “On triangle path convexity in graphs,” Discrete Mathematics, vol. 206, no. 1–3, pp. 91–95, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. F. M. Malvestuto, “Canonical and monophonic convexities in hypergraphs,” Discrete Mathematics, vol. 309, no. 13, pp. 4287–4298, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. M. Changat, H. M. Mulder, and G. Sierksma, “Convexities related to path properties on graphs,” Discrete Mathematics, vol. 290, no. 2-3, pp. 117–131, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. B. Kannan and M. Changat, “Hull numbers of path convexities on graphs,” in Proceedings of the Workshop on Convexity in Discrete Structures, Thirunvananthapuram (Kerala), India, 2006, M. Changat, X. Klavzar, H. M. Mulder, and A. Vijayakumar, Eds., pp. 11–23, Ramanujan Mathematical Society, Kerala, India, 2008. View at Zentralblatt MATH · View at MathSciNet
  10. M. C. Dourado, F. Protti, and J. L. Szwarcfiter, “Algorithmic aspects of monophonic convexity,” Electronic Notes in Discrete Mathematics C, vol. 30, pp. 177–182, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. M. C. Dourado, F. Protti, and J. L. Szwarcfiter, “Complexity results related to monophonic convexity,” Discrete Applied Mathematics, vol. 158, no. 12, pp. 1268–1274, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. P. Duchet, “Hypergraphs,” in Handbook of Combinatorics. Volume I, R. L. Graham, M. Grötschel, and L. Lovász, Eds., pp. 381–432, North Holland, Amsterdam, The Netherlands, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. T. Kloks, Treewidth. LNCS 842, Springer Verlag, New York, NY, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. Beeri, R. Fagin, D. Maier, and M. Yannakakis, “On the desirability of acyclic database schemes,” Journal of the ACM, vol. 30, no. 3, pp. 479–513, 1983. View at Publisher · View at Google Scholar · View at Scopus
  15. R. E. Tarjan and M. Yannakakis, “Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs,” SIAM Journal on Computing, vol. 13, no. 3, pp. 566–579, 1984. View at Google Scholar · View at Scopus
  16. D. Maier and J. D. Ullman, “Connections in acyclic hypergraphs,” Theoretical Computer Science, vol. 32, no. 1-2, pp. 185–199, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. F. Ardila and E. Maneva, “Pruning processes and a new characterization of convex geometries,” Discrete Mathematics, vol. 309, no. 10, pp. 3083–3091, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. F. M. Malvestuto and M. Moscarini, “A fast algorithm for query optimization in universal-relation databases,” Journal of Computer and System Sciences, vol. 56, no. 3, pp. 299–309, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. H.-G. Leimer, “Optimal decomposition by clique separators,” Discrete Mathematics, vol. 113, no. 1–3, pp. 99–123, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. F. M. Malvestuto and M. Moscarini, “Decomposition of a hypergraph by partial-edge separators,” Theoretical Computer Science, vol. 237, no. 1-2, pp. 57–79, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus