Squashing maximum packings of 6-cycles into maximum packings of triples - Lindner, Charles Curtis (Ars mathematica contemporanea, 2016)
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 ?$n \ge 6$?, there is a max packing of ?$K_n$? with 6-cycles that can be squashed into a maximum packing of ?$K_n$? with triples.
Keywords: maksimalna pakiranja 6-ciklov; maksimalna pakiranja trojic; maximum packing with 6-cycles; maximum packing with triples