Embedding Partial Graph Designs, Block Designs, and Triple Systems with λ > 1
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 385-391
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A general embedding technique for graph designs and block designs is developed, which transforms the embedding problem for partial designs with ƛ > 1 into the embedding problem for partial designs with ƛ = 1. Given an embedding technique for n-element partial block designs with ƛ = 1 into block designs with f(n) elements, the transformation produces a technique which embeds an «-element partial design with ƛ > 1 and block size k into a design with at most /(3k-1ƛn2) elements. For graph designs and block designs with k > 3, a finite embedding method results. For triple systems, a quadratic embedding technique is obtained immediately; the best previous result here was exponential. Finally, for partial triple systems, Mendelsohn triple systems, and directed triple systems, these quadratic embeddings are improved to linear using a colouring technique.
Colbournt, C. J.; Hamm, R. C.; Lindner, C. C.; Lindner, C. C.; Rodger, C. A. Embedding Partial Graph Designs, Block Designs, and Triple Systems with λ > 1. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 385-391. doi: 10.4153/CMB-1986-061-4
@article{10_4153_CMB_1986_061_4,
author = {Colbournt, C. J. and Hamm, R. C. and Lindner, C. C. and Lindner, C. C. and Rodger, C. A.},
title = {Embedding {Partial} {Graph} {Designs,} {Block} {Designs,} and {Triple} {Systems} with \ensuremath{\lambda} > 1},
journal = {Canadian mathematical bulletin},
pages = {385--391},
year = {1986},
volume = {29},
number = {4},
doi = {10.4153/CMB-1986-061-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-061-4/}
}
TY - JOUR AU - Colbournt, C. J. AU - Hamm, R. C. AU - Lindner, C. C. AU - Lindner, C. C. AU - Rodger, C. A. TI - Embedding Partial Graph Designs, Block Designs, and Triple Systems with λ > 1 JO - Canadian mathematical bulletin PY - 1986 SP - 385 EP - 391 VL - 29 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-061-4/ DO - 10.4153/CMB-1986-061-4 ID - 10_4153_CMB_1986_061_4 ER -
%0 Journal Article %A Colbournt, C. J. %A Hamm, R. C. %A Lindner, C. C. %A Lindner, C. C. %A Rodger, C. A. %T Embedding Partial Graph Designs, Block Designs, and Triple Systems with λ > 1 %J Canadian mathematical bulletin %D 1986 %P 385-391 %V 29 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-061-4/ %R 10.4153/CMB-1986-061-4 %F 10_4153_CMB_1986_061_4
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