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Bounding graphical t-wise balanced designs

✍ Scribed by Leo G. Chouinard II

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 167 KB
Volume: 159
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00117-f

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✦ Synopsis

Let X be the edges of the complete graph K, on n vertices, provided with the natural action of S,, the automorphism group of K,. A t-wise balanced design (X,.8) with parameters t-((~), K, )J is said to be 9raphical if.~ is fixed under the action of S,. We show that for any pair (t, 2) with t > 1 or 2 odd, there cannot exist a non-trivial graphical t-((~), K,)J design with n ~> 2t + 2 + 4. Thus, in particular, for each such pair (t, 2) there are only a finite number of non-trivial graphical t-(v, K, 2) designs. If we further assume no repeated blocks, then for all cases with t > 1 or )~ ~ 2, there do not exist non-trivial graphical t-((g), K, 2) designs with n >~ 2t + 2 + 4.

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