Matching divisible designs with block size four

作者:Dukes, Peter J.*; Feng, Tao; Ling, Alan C. H.
来源:Discrete Mathematics, 2016, 339(2): 790-799.
DOI:10.1016/j.disc.2015.10.011

摘要

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.