Matching divisible designs with block size four

We consider edge-decompositions of the graph join of several equal-sized one-factors into cliques of a prescribed size. These objects are variants of group divisible designs and have applications to packings, coverings, and embeddings. Assuming block (clique) size four, we show that the obvious divi...

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Bibliographic Details
Published in:Discrete mathematics 2016-02, Vol.339 (2), p.790-799
Main Authors: Dukes, Peter J., Feng, Tao, Ling, Alan C.H.
Format: Article
Language:English
Subjects:
Edge-decomposition
Graph factorization
Group divisible design
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Summary:We consider edge-decompositions of the graph join of several equal-sized one-factors into cliques of a prescribed size. These objects are variants of group divisible designs and have applications to packings, coverings, and embeddings. Assuming block (clique) size four, we show that the obvious divisibility and counting conditions are sufficient for the existence of such designs.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2015.10.011