Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Strongly regular graphs from differences of quadrics

In this note strongly regular graphs with new parameters are constructed using nested "blown up" quadrics in projective spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

Tenuous threads, small miracles

With the new Noosa Youth Centre, Deborah Fisher Architects has woven a small yet sophisticated building out of highly constrained and complex circumstances. Douglas Neale explores a project that convinces through its modesty.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

Cross-reactivity of Sydney funnel-web spider antivenom: neutralization of the in vitro toxicity of other Australian funnel-web (Atrax and Hadronyche) spider venoms

Australian funnel-web spiders are recognized as one of the most venomous spiders to humans world-wide. Funnel-web spider antivenom (FWS AV) reverses clinical effects of envenomation from the bite of Atrax robustus and a small number of related Hadronyche species. This study assessed the in vitro efficacy of FWS AV in neutralization of the effects of funnel-web spider venoms, collected from various locations along the eastern seaboard of Australia, in an isolated chick biventer cervicis nerve-muscle preparation. Venoms were separated by SDS-PAGE electrophoresis to compare protein composition and transblotted for Western blotting and incubation with FWS AV. SDS-PAGE of venoms revealed similar low and high molecular weight protein bands. Western blotting with FWS AV showed similar antivenom binding with protein bands in all the venoms tested. Male funnel-web spider venoms (7/7) and female venoms (5110) produced muscle contracture and fasciculation when applied to the nerve-muscle preparation. Venom effects were reversed by subsequent application of FWS AV or prevented by pretreatment of the preparation with antivenom. FWS AV appears to reverse the in vitro toxicity of a number of funnel-web spider venoms from the eastern seaboard of Australia. FWS AV should be effective in the treatment of envenomation from most, if not all, species of Australian funnel-web spiders. (C) 2001 Elsevier Science Ltd. All rights reserved.