A Hamiltonian cycle system of the complete graph minus a 1–factor $K_{2v} − I$ (briefly, an HCS(2v)) is 2-pyramidal if it admits an automorphism group of order 2v − 2 fixing two vertices. In spite of the fact that the very first example of an HCS(2v) is very old and 2-pyramidal, a thorough investigation of this class of HCSs is lacking. We give first evidence that there is a strong relationship between 2-pyramidal HCS(2v) and 1-rotational Hamiltonian cycle systems of the complete graph $K_{2v−1}$. Then, as main result, we determine the full automorphism group of every 2-pyramidal HCS(2v). This allows us to obtain an exponential lower bound on the number of non-isomorphic 2-pyramidal HCS(2v).

On 2-pyramidal Hamiltonian cycle systems / Bailey, Rosemary; Buratti, Marco; Rinaldi, Gloria; Traetta, Tommaso. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - 21:4(2014), pp. 747-758.

On 2-pyramidal Hamiltonian cycle systems

BURATTI, Marco;
2014

Abstract

A Hamiltonian cycle system of the complete graph minus a 1–factor $K_{2v} − I$ (briefly, an HCS(2v)) is 2-pyramidal if it admits an automorphism group of order 2v − 2 fixing two vertices. In spite of the fact that the very first example of an HCS(2v) is very old and 2-pyramidal, a thorough investigation of this class of HCSs is lacking. We give first evidence that there is a strong relationship between 2-pyramidal HCS(2v) and 1-rotational Hamiltonian cycle systems of the complete graph $K_{2v−1}$. Then, as main result, we determine the full automorphism group of every 2-pyramidal HCS(2v). This allows us to obtain an exponential lower bound on the number of non-isomorphic 2-pyramidal HCS(2v).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654673
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