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−1)/2 with 1≤k≤v/2. The decompositions are required to admit an automorphism group Γ acting sharply transitively on the set of vertices. Here Γ 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 Γ 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 admissible value of k when v is odd and Γ is an arbitrary group of odd order possessing a subgroup of order gcd(k,v).
On the existence spectrum for sharply transitive G-designs, G a [k]-matching / Bonisoli, Arrigo; Bonvicini, Simona. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 332:(2014), pp. 60-68. [10.1016/j.disc.2014.05.021]
On the existence spectrum for sharply transitive G-designs, G a [k]-matching
BONISOLI, Arrigo;BONVICINI, Simona
2014
Abstract
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−1)/2 with 1≤k≤v/2. The decompositions are required to admit an automorphism group Γ acting sharply transitively on the set of vertices. Here Γ 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 1File | Dimensione | Formato | |
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