A bowtie is a graph consisting of two 3-cycles sharing a vertex. A kite is a connected graph consisting of a 3-cycle together with a single edge. Let H be a kite or a bowtie. We study H-decompositions of the complete graphKv admitting an automorphism group G acting (sharply) transitively on the vertices of Kv. We give necessary conditions, involving the rank of the group G and the decomposition into disjoint cycles of the elements of G, which yield non-existence results. By using constructions we obtain existence results.
Symmetric decompositions of the complete graph / Ruini, Beatrice. - STAMPA. - (2010), pp. 213-213. (Intervento presentato al convegno Combinatorics 2010 tenutosi a Verbania nel 28/06/2010-30/06/2010).
Symmetric decompositions of the complete graph
RUINI, Beatrice
2010
Abstract
A bowtie is a graph consisting of two 3-cycles sharing a vertex. A kite is a connected graph consisting of a 3-cycle together with a single edge. Let H be a kite or a bowtie. We study H-decompositions of the complete graphKv admitting an automorphism group G acting (sharply) transitively on the vertices of Kv. We give necessary conditions, involving the rank of the group G and the decomposition into disjoint cycles of the elements of G, which yield non-existence results. By using constructions we obtain existence results.
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