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

Curt C. Lindner, Giovanni Lo Faro, Antoinette Tripodi


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 Kn with 6-cycles into maximum packings of Kn with triples. More specifically, we establish that for each n ≥ 6, there is a max packing of Kn with 6-cycles that can be squashed into a maximum packing of Kn with triples.


Maximum packing with triples, maximum packing with 6-cycles

Full Text:


DOI: https://doi.org/10.26493/1855-3974.706.33d

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications