0,7

Verified for n=11, 12 by Shengjun Pan and R. Bruce Richter, in "The Crossing Number of K_11 is 100", submitted. Still dubious for n >= 13.

Also the sum of the dimensions of the irreducible representations of su(3) that first occur in the [n-5]th tensor power of the tautological representation. - james dolan (jdolan(AT)math.ucr.edu), Jun 02 2003

P. Erdos and R. K. Guy, Crossing number problems, Amer. Math. Monthly, 80 (1973), 52-58.

R. K. Guy, The crossing number of the complete graph, Bull. Malayan Math. Soc., Vol. 7, pp. 68-72, 1960.

A. Owens, On the biplanar crossing number, IEEE Trans. Circuit Theory, 18 (1971), 277-280.

T. L. Saaty, The number of intersections in complete graphs, Engrg. Cybernetics 9 (1971), no. 6, 1102-1104 (1972).; translated from Izv. Akad. Nauk SSSR Tehn. Kibernet. 1971, no. 6, 151-154 (Russian). Math. Rev. 58 #21749.

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

J. Dolan et al., su(3) and Zarankiewicz's conjecture

T. L. Saaty, The Minimum Number Of Intersections In Complete Graphs

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

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

E. Weisstein, Zarankiewicz's Conjecture.html

Drago Bokal, Gasper Fijavz and David R. Wood, The Minor Crossing Number of Graphs with an Excluded Minor, math.CO/0609707.

It is not known if A000241 and A028723 agree. Cf. A007333, A014540, A030179.

Cf. A121021.

Sequence in context: A093446 A132920 A127645 this_sequence A028723 A057578 A015635

Adjacent sequences: A000238 A000239 A000240 this_sequence A000242 A000243 A000244

nonn,nice

njas

Bokal et al. link from Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 08 2006