Topological graphs with no large grids

Graphs and Combinatorics

Volumn 21, Issue 3, 2005, Pages 355-364

  Pach, János ^a   Pinchasi, Rom ^b   Sharir, Micha ^a,c   Tóth, Géza ^d  

^a NEW YORK UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

^d INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

Crossing edges; Topological graphs

Indexed keywords

EID: 27544442925     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00373-005-0616-1     Document Type: Article

References (9)

1. Agarwal, P.K., Aronov, B., Pach, J., Pollack, R., Sharir, M.: Quasi-planar graphs have a linear number of edges. Combinatorica 17, 1-9 (1997)
2. Braß, P., Károlyi, G., Valtr, P.: A Turán-type extremal theory of convex geometric graphs. In: Discrete and Computational Geometry - The Goodman-Pollack Festschrift, B. Aronov et al., (eds.), Algorithms and Combinatorics 25, Springer, Berlin, 2003, pp. 275-300
3. Pach, J.: Geometric graph theory. In: Surveys in Combinatorics, 1999, J.D. Lamb, D.A. Preece, (eds.), London Mathematical Society Lecture Notes 267, Cambridge University Press, Cambridge, 1999, pp. 167-200
4. Pach, J., Radoičić, R., Tóth, G.: Relaxing planarity for topological graphs. In: Discrete and Computational Geometry, J. Akiyama, M. Kano (eds.), Lecture Notes in Computer Science 2866 Springer, Berlin, 2003, 221-232
5. Pach, J., Radoičić, R., Tóth, G.: A generalization of quasi-planarity. In: Towards a Theory of Geometric Graphs, J. Pach (ed.), Contemporary Mathematics 342, AMS, 2004, 177-183
6. Pach, J., Pinchasi, R., Tardos, G., Tóth, G.: Geometric graphs with no self-intersecting path of length three. In: Graph Drawing, M.T. Goodrich, S.G. Kobourov (eds.), Lecture Notes in Computer Science 2528, Springer, Berlin, 2002, pp. 295-311.
7. Also in: European Journal of Combinatorics 25, 793-811 (2004)
8. Pach, J., Tóth, G.: Graphs drawn with few crossings per edge. Combinatorica 17, 427-439 (1997)
9. Schaefer, M., Stefankovič, D.: Decidability of string graphs. In: Proceedings of the 33rd Annual Symposium on the Theory of Computing (STOC 2001), 2001, pp. 241-246