Which crossing number is it anyway?

Journal of Combinatorial Theory. Series B

Volumn 80, Issue 2, 2000, Pages 225-246

  Pach, János ^a,b   Tóth, Géza ^c  

^a NEW YORK UNIVERSITY   (United States)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^c RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034311833     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1006/jctb.2000.1978     Document Type: Article

References (23)

1. Ajtai M., Chvátal V., Newborn M., Szemerédi E. Crossing-free subgraphs. Theory and Practice of Combinatorics. 1982;North-Holland Math. Stud. North-Holland, Amsterdam/New York. p. 9-12.
2. Bhatt S. N., Leighton F. T. A framework for solving VLSI graph layout problems. J. Comput. System Sci. 28:1984;300-343.
3. Bienstock D. Some provably hard crossing number problems. Discrete Comput. Geom. 6:1991;443-459.
4. Bienstock D., Dean N. New results on rectilinear crossing numbers and plane embeddings. J. Graph Theory. 16:1992;389-398.
5. Bienstock D., Dean N. Bounds for rectilinear crossing numbers. J. Graph Theory. 17:1993;333-348.
6. Bondy J. A., Murty U. S. R. Graph Theory with Applications. 1976;Am. Elsevier, New York.
7. Cairns G., Nikolayevsky Y. Bounds for generalized thrackles. Discrete Comput. Geom. 23:2000;191-206.
8. Chojnacki Ch., Hanani A. Über wesentlich unplättbare Kurven im dreidimensionalen Raume. Fund. Math. 23:1934;135-142.
9. Fáry I. On straight line representation of planar graphs. Acta Univ. Szeged. Sect. Math. 11:1948;229-233.
10. Garey M. R., Johnson D. S. Crossing number is NP-complete. SIAM J. Algebraic. Discrete Methods. 4:1983;312-316.
11. Garey M. R., Johnson D. S., Stockmeyer L. J. Some simplified NP-complex graph problems. Theoret. Comput. Sci. 1:1976;237-267.
12. Guy R. K. The decline and fall of Zarankiewicz's theorem. Proof Techniques in Graph Theory. 1969;Academic Press, New York. p. 63-69.
13. Jensen H. F. An upper bound for the rectilinear crossing number of the complete graph. J. Combin. Theory Ser. B. 10:1971;212-216.
14. Leighton F. T. Complexity Issues in VLSI. 1983;MIT Press, Cambridge.
15. Leighton F. T. New lower bound techniques for VLSI. Math. Systems Theory. 17:1984;47-70.
16. Lovász L., Pach J., Szegedy M. On Conway's thrackle conjecture. Discrete Comput. Geom. 18:1997;369-376.
17. Pach J., Tóth G. Graphs drawn with few crossing per edge. Combinatorica. 17:1997;427-439.
18. Pach J., Tóth G. Which crossing number is it, anyway? Proceedings, 39th Annual Symposium on Foundations of Computer Science. 1998;. p. 617-626.
19. Richter R. B., Thomassen C. Relations between crossing numbers of complete and complete bipartite graphs. Amer. Math. Monthly. February 1997;131-137.
20. Shakrokhi F., Sýkora O., Székely L. A., Vrťo I. Crossing numbers: Bounds and applications. Intuitive Geometry (Budapest, 1995). Bolyai Soc. Math. Stud. 6:1995;János Bolyai Math. Soc. Budapest. p. 179-206.
21. Turán P. A note of welcome. J. Graph Theory. 1:1977;7-9.
22. Tutte W. T. Toward a theory of crossing numbers. J. Combin. Theory. 8:1970;45-53.
23. White A. T., Beineke L. W. Topological graph theory. Beineke L. W., Wilson R. J. Selected Topics in Graph Theory. 1983;15-49 Academic Press, London/New York.