On the existence spectrum for sharply transitive G-designs, G a [k]-matching
- Bonisoli, Arrigo
- Bonvicini, Simona
DOIAbstract
In this paper we consider decompositions of the complete graph Kv into matchings of uniform cardinality k. They can only exist when k is an admissible value, that is a divisor of v(v 121)/2 with 1 64k 64v/2. The decompositions are required to admit an automorphism group \u393 acting sharply transitively on the set of vertices. Here \u393 is assumed to be either non-cyclic abelian or dihedral and we obtain necessary conditions for the existence of the decomposition when k is an admissible value with 1<k<v/2. Differently from the case where \u393 is a cyclic group, these conditions do exclude existence in specific cases. On the other hand we produce several constructions for a wide range of admissible values, in particular for every admissibl...
Add to ORKG