Squashing maximum packings of 6-cycles into maximum packings of triples

A  6 -cycle is said to be squashed if we identify a pair of opposite vertices and name one of them with the other (and thereby turning the  6 -cycle into a pair of triples with a common vertex). The squashing problem for  6 -cycle systems was introduced by C. C. Lindner, M. Meszka and A. Rosa and completely solved by determining the spectrum. In this paper, by employing PBD and GDD-constructions and filling techniques, we extend this result by squashing maximum packings of  K n  with  6 -cycles into maximum packings of  K n  with triples. More specifically, we establish that for each  n  ≥ 6 , there is a max packing of  K n  with  6 -cycles that can be squashed into a maximum packing of  K n  with triples.

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