86b:47008 Bollobas, B.; Partington, J. R. Inequalities for quadratic polynomials in Hermitian and dissipative operators. Adv. in Math. 51 (1984), no. 3, 271--280. 47A30 (47B15)
49 #129 Bollobás, Béla; Erdös, Paul. On the structure of edge graphs. Bull. London Math. Soc. 5 (1973), 317--321. 05C35
There are also some disjoint paths of length 4, e.g. Partington, Baratchart, Saff, Clunie, Erdös; and Partington, Chalendar, Chevreau, Shields, Erdös.
Perhaps more surprisingly, my Einstein number is 3 (via Bollobás and E.G. Straus), my Hardy number is 4 (via Bollobás, Klee and E.M. Wright), my Turing number is 6 (via Baratchart, Saff, Varga, Wilkinson and Newman), and my Hilbert number is 6 (via Ransford, Berndtsson, Chang, Lax and Courant).
Last updated on August 1st 2005 by Jonathan Partington