J. Pach, J. Spencer, and G. Toth. New bounds for crossing numbers,. Discrete Comput. Geom., 24:623-644, 2000. Home/Search Document Details and Download
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Biplanar Crossing Numbers I: A Survey of Results and Problems - Czabarka, Sýkora (Correct)
....of Theorem 3.2 in [20] one obtains the following biplanar counterpart of the Leighton [10] and Ajtai et al. 2] bound: for all c 6, if m cn, then c Gamma 6 c : 7) For somewhat denser graphs one can improve (7) using the Pach T oth s results cited above. Pach, Spencer and T oth [17] proved a conjecture of Simonovits, improving the bound of (7) If G has girth 2r and m 4n, then cr(G) Omega : 8) It is easy to see that (8) also holds for cr 2 instead of cr, if m 8n. Lower bounds for the crossing number based on the counting method [20] provide similar arguments ....
Pach, J., Spencer, J., and T'oth, G., New bounds on crossing numbers, Discrete Comp. Geom. 24 (2000), 623--644.
Toward the Rectilinear Crossing Number of K n : New.. - Brodsky, Durocher.. (2000) (Correct)
.... same can be said for an arbitrary graph when the edges are assumed to be line segments [Bie91] Recent exciting work on the general crossing number problem (where edges are simply homeomorphs of the unit interval [0; 1] rather than line segments) has been accomplished by Pach, Spencer, and T oth [PST99], who give a tight lower bound for the crossing number of families of graphs with certain forbidden subgraphs. We study the specific instance of determining the rectilinear crossing number of K n , denoted cr(K n ) and we offer embeddings with few edge crossings. The difficulty of determining ....
J. Pach, J. Spencer, and G. T'oth. New bounds on crossing numbers. In Proceedings of the 15th annual symposium on Computational Geometry(Miami, Florida), pages 124--133. ACM Press, New York, 1999.
Crossing Number, Pair-Crossing Number, and Expansion - Kolman, Matousek (Correct)
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J. Pach, J. Spencer, and G. Toth. New bounds for crossing numbers,. Discrete Comput. Geom., 24:623-644, 2000.
Crossing Number, Pair-Crossing Number, and Expansion - Kolman, Matousek (2003) (Correct)
No context found.
J. Pach, J. Spencer, and G. Toth. New bounds for crossing numbers,. Discrete Comput. Geom., 24:623-644, 2000.
Biplanar Crossing Numbers I: A Survey of Results and.. - Czabarka, Sykora.. (Correct)
No context found.
Pach, J., Spencer, J., and T'oth, G., New bounds on crossing numbers, Discrete Comp. Geom. 24 (2000), 623--644.
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