Squashing minimum coverings of 6-cycles into minimum coverings of triples

Abstract

A 6-cycle is said to be squashed if we identify a pair of opposite vertices and name one of them with the other (thereby turning the 6-cycle into a pair of triples with a common vertex). A 6-cycle can be squashed in six different ways. The spectrum for 6-cycle systems that can be squashed into Steiner triple systems has been determined by Lindner et al.(J Comb Des 22:189-195, 2014). The squashing of maximum packings of K (n) with 6-cycles into maximum packings of K (n) with triples has also been fully dealt with by Lindner et al. (Squashing maximum packings of 6-cycles into maximum packings of triples (submitted)). The object of this paper is to extend these results to minimum coverings of K (n) with 6-cycles into minimum coverings of K (n) with triples. We give a complete solution.