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The Doyen-Wilson theorem for maximum packings of Kn with 4-cycles

✍ Scribed by H.-L. Fu; C.C. Lindner

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
704 KB
Volume
183
Category
Article
ISSN
0012-365X

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✦ Synopsis

Necessary and sufficient conditions are given to embed a maximum packing of K,, with 4-cycles into a maximum packing of K, with 4-cycles, both when the leave of the given packing is preserved, and when the leave of the given packing is not necessarily preserved.

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Let (X; B) be a -fold block design with block size four and deÿne sets B(C) and E(K4 \ C) as follows: for each block b ∈ B, partition b into a 4-cycle and a pair of disjoint edges and place the 4-cycle in B(C) and the 2 disjoint edges in E(K4 \ C). If we can reassemble the edges belonging to E(K4 \