Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 154015, 10 pages
doi:10.1155/2009/154015
Research Article
An Evolutionary Formulation of the Crossing Number Problem
Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia
Received 24 September 2008; Revised 31 March 2009; Accepted 2 July 2009
Academic Editor: B. Sagar
Copyright © 2009 Che Sheng Gan et al. 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
- G. Chartrand and L. Lesniak, Graphs & Digraphs, Chapman & Hall, London, UK, 3rd edition, 1996. View at Zentralblatt MATH · View at MathSciNet
- W. T. Tutte, “Toward a theory of crossing numbers,” Journal of Combinatorial Theory Series B, vol. 8, pp. 45–53, 1970. View at Zentralblatt MATH · View at MathSciNet
- P. Turán, “A note of welcome,” Journal of Graph Theory, vol. 1, pp. 7–9, 1977. View at Publisher · View at Google Scholar
- M. R. Garey and D. S. Johnson, “Crossing number is NP-complete,” SIAM Journal on Algebraic and Discrete Methods, vol. 4, no. 3, pp. 312–316, 1983. View at Zentralblatt MATH · View at MathSciNet
- R. K. Guy, “Crossing numbers of graphs,” in Graph Theory and Applications, pp. 111–124, Springer, New York, NY, USA, 1972. View at Zentralblatt MATH · View at MathSciNet
- S. Pan and R. B. Richter, “The crossing number of K11 is 100,” Journal of Graph Theory, vol. 56, no. 2, pp. 128–134, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- F. C. Harris Jr. and R. H. Cynthia, “A proposed algorithm for calculating the minimum crossing number of a graph,” in Proceedings of the 8th Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms, and Applications, Kalamazoo, Mich, USA, June 1996.
- C. Gutwenger and P. Mutzel, “An experimental study of crossing minimization heuristics,” in Graph Drawing, G. Liotta, Ed., vol. 2912 of Lecture Notes in Computer Science, pp. 13–24, Springer, Berlin, Germany, 2004. View at MathSciNet
- U. Tadjiev, Parallel computation and graphical visualization of the minimum crossing number of a graph, M.S. thesis, University of Nevada, 1998.
- D. Archdeacon, December 2003, http://www.emba.uvm.edu/~archdeac/problems/crosskn.htm.