On the existence spectrum for sharply transitive G-designs, G a [k]-matching

In this paper we consider decompositions of the complete graph K"v 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 @C acting sharply transitively on the set of vertices. Here @C 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

[1]  P. Cameron.  Parallelisms Of Complete Designs , 1976 .

[2]  Marco Buratti,et al.  1-Rotational k-Factorizations of the Complete Graph and New Solutions to the Oberwolfach Problem , 2008 .

[3]  Marco Buratti,et al.  Dihedral Hamiltonian Cycle Systems of the Cocktail Party Graph , 2013 .

[4]  Mathieu Bogaerts,et al.  Cyclic and Dihedral 1-Factorizations of Multipartite Graphs , 2011, Electron. J. Comb..

[5]  Alan Hartman,et al.  Cyclic One-Factorization of the Complete Graph , 1985, Eur. J. Comb..

[6]  Marco Buratti,et al.  The Structure of $$2$$2-Pyramidal $$2$$2-Factorizations , 2015, Graphs Comb..

[7]  Anita Pasotti,et al.  Symmetric 1-factorizations of the complete graph , 2010, Eur. J. Comb..

[8]  Peter Adams,et al.  A survey on the existence of G‐Designs , 2008 .

[9]  Simona Bonvicini,et al.  Frattini-based starters in 2-groups , 2008, Discret. Math..

[10]  Domenico Labbate,et al.  One‐factorizations of complete graphs with vertex‐regular automorphism groups , 2002 .

[11]  Marco Buratti.  Cycle decomposition with a sharply vertex transitive automorphism group , 2006 .

[12]  Marco Buratti,et al.  Abelian 1-Factorizations of the Complete Graph , 2001, Eur. J. Comb..

[13]  Victor H. Moll,et al.  Arithmetic Properties of Plane Partitions , 2011, Electron. J. Comb..

[14]  W. Scott,et al.  Group Theory. , 1964 .

[15]  Gloria Rinaldi,et al.  Nilpotent 1‐factorizations of the complete graph , 2005 .

[16]  Philip A. Leonard,et al.  Adders for the patterned starter in nonabelian groups , 1976 .

[17]  Gábor Korchmáros,et al.  Sharply transitive 1‐factorizations of the complete graph with an invariant 1‐factor , 1994 .