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25th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
December 4-8, 2000
University of Canterbury
Christchurch, New Zealand

Organizers
Charles Semple, Mike Steel

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Minimal PBDs with Specified Longest Block Length
by
Ralph G. Stanton
University of Manitoba, Winnipeg, CANADA

If one is given v elements, it is an important problem to determine the minimal pairwise balanced design under the restriction that the largest block size is a specified integers k. This is equivalent to finding the clique number for covering the complete graph Kv with subcliques of which the largest subclique has size k.

The problem splits into 2 parts. If k is less than root v, then one tries to pack in a lot of blocks of length k.

If k is greater than root v, then the long block of length k takes a special role, and the solution involves a large number of short blocks that meet the long block.

We shall discuss the second case, using a unified approach that includes a number of earlier results.

Date received: October 30, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafn-22.