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Minimum embedding of P 3 ‐designs into (K 4 —e)‐designs
Author(s) -
Colbourn Charles J.,
Ling Alan C. H.,
Quattrocchi Gaetano
Publication year - 2003
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.10044
Subject(s) - embedding , mathematics , combinatorics , discrete mathematics , arithmetic , computer science , artificial intelligence
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