Table of Contents
Journal of Discrete Mathematics
Volume 2014 (2014), Article ID 731519, 5 pages
http://dx.doi.org/10.1155/2014/731519
Research Article

Noncrossing Monochromatic Subtrees and Staircases in 0-1 Matrices

1Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, USA
2Department of Mathematics, Pomona College, 640 North College Avenue, Claremont, CA 91711, USA
3Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O. Box 127, Budapest 1364, Hungary
4Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA

Received 16 September 2013; Accepted 12 November 2013; Published 23 January 2014

Academic Editor: Wai Chee Shiu

Copyright © 2014 Siyuan Cai 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

  1. J. Pach and P. K. Agarwal, Combinatorial Geometry, John Wiley & Sons, New York, NY, USA, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  2. P. Eades and S. Whitesides, “Drawing graphs in two layers,” Theoretical Computer Science, vol. 131, no. 2, pp. 361–374, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. N. Alon and P. Erdös, “Disjoint edges in geometric graphs,” Discrete & Computational Geometry, vol. 4, no. 4, pp. 287–290, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. Brass, G. Károlyi, and P. Valtr, “A Turán-type extremal theory of convex geometric graphs,” in Discrete and Computational Geometry: Algorithms Combination, vol. 25, pp. 275–300, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Gyárfás, “Ramsey and Turán-type problems for non-crossing subgraphs of bipartite geometric graphs,” Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, vol. 54, pp. 45–56, 2011. View at Google Scholar · View at MathSciNet
  6. G. Károlyi, J. Pach, and G. Tóth, “Ramsey-type results for geometric graphs. I,” Discrete & Computational Geometry, vol. 18, no. 3, pp. 247–255, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Károlyi, J. Pach, G. Tóth, and P. Valtr, “Ramsey-type results for geometric graphs. II,” Discrete & Computational Geometry, vol. 20, no. 3, pp. 375–388, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. Kupitz, “On pairs of disjoint segments in convex position in the plane, Convexityand Graph theory (Jerusalem 1981),” Annals of Discrete Mathematics, vol. 20, pp. 203–208, 1984. View at Google Scholar
  9. A. Kaneko and M. Kano, “Discrete geometry on red and blue points in the plane—a survey,” in Discrete and Computational Geometry, Algorithms Combininatorics, vol. 25, pp. 551–570, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Harary and A. Schwenk, “A new crossing number for bipartite graphs,” Utilitas Mathematica, vol. 1, pp. 203–209, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet