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, Meszka and Rosa [From squashed 6-cycles to Steiner triple systems, J. Combin. Des. [6]]. 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, Lo Faro and Tripodi [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 Kn with 6-cycles into minimum coverings of Kn with triples. We give a complete solution.