1,6

The values a(19) and a(21) were obtained by Aichholzer et al. in 2006. The value a(18) is claimed by the Rectilinear Crossing Number project after months of distributed computing. This was confirmed by Abrego et al., they also found the values a(20) and a(22) to a(27). The next unknown entry, a(28), is either 7233 or 7234. - Bernardo M. Abrego (bernardo.abrego(AT)csun.edu), May 05 2008

O. Aichholzer, F. Aurenhammer, and H. Krasser. Progress on rectilinear crossing numbers. Technical report, IGI-TU Graz, Austria, 2001.

D. Bienstock and N. Dean, Bounds for rectilinear crossing numbers, J. Graph Theory 17 (1993) 333-348

A. Brodsky, S. Durocher and E. Gethner, Toward the rectilinear crossing number of K_n..., Discrete Math. 262 (2003), 59-77.

M. Gardner, Crossing Numbers. Ch. 11 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, 1986.

H. F. Jensen, An Upper Bound for the Rectilinear Crossing Number of the Complete Graph, J. Comb. Th. Ser. B 10, 212-216, 1971.

C. Thomassen, Embeddings and minors, pp. 301-349 of R. L. Graham et al., eds., Handbook of Combinatorics, MIT Press.

B.M. Abrego, S. Fernandez-Merchant, J. Lea��Á��os and G. Salazar, The maximum number of halving lines and the rectilinear crossing number of K_n for n <= 27, Electronic Notes in Discrete Mathematics, 30 (2008), 261-266.

O. Aichholzer, J. Garcia, D. Orden, P. Ramos, New lower bounds for the number of <= k-edges and the rectilinear crossing number of K_n. Discrete & Computational Geometry 38 (2007), 1-14.

O. Aichholzer, Crossing number project

O. Aichholzer, F. Aurenhammer and H. Krasser, Progress on rectilinear crossing numbers.

O. Aichholzer, F. Aurenhammer and H. Krasser, On the Rectilinear Crossing Number

O. Aichholzer and H. Krasser, The point set order type data base: a collection of applications and results, pp. 17-20 in Abstracts 13-th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

D. Archdeacon, The rectilinear crossing number

A. Brodsky, S. Durocher and E. Gethner, The Rectilinear Crossing Number of K_{10} is 62, Electronic J. Combin., #R23, 2001.

D. Garber, The Orchard crossing number of an abstract graph

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

E. Weisstein, Zarankiewicz's Conjecture.html

Cf. A000241, A030179.

Sequence in context: A049749 A058058 A062748 this_sequence A115238 A005994 A080010

Adjacent sequences: A014537 A014538 A014539 this_sequence A014541 A014542 A014543

nonn,nice,hard

Eric Weisstein (eric(AT)weisstein.com)

102 from Oswin Aichholzer (oswin.aichholzer(AT)tugraz.at), Aug 14, 2001

153 from Hannes Krasser (hkrasser(AT)igi.tu-graz.ac.at), Sep 17 2001

More terms from Eric Weisstein (eric(AT)weisstein.com), Nov 30 2006

More terms from Bernardo M. Abrego (bernardo.abrego(AT)csun.edu), May 05 2008