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Minimum embedding of P3-designs into (K4—e)-designs

✍ Scribed by Charles J. Colbourn; Alan C. H. Ling; Gaetano Quattrocchi

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 173 KB
Volume: 11
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10044

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✦ Synopsis

Abstract

A (K~4~ − e)‐design on v + w points embeds a P~3~‐design on v points if there is a subset of v points on which the K~4~ − e blocks induce the blocks of a P~3~‐design. It is shown that w ≥ ¾(v − 1). When equality holds, the embedding design is easily constructed. In this paper, the next case, when w = ¾__v__, is settled with finitely many exceptions. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 352–366, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10044

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