We give an explicit solution to the existence problem for 1-rotational k-cycle systems of order v < 3k with k odd and v ≠ 2k + 1. We also exhibit a 2-rotational k-cycle system of order 2k + 1 for any odd k. Thus, for k odd and any admissible v < 3k there exists a 2-rotational k-cycle system of order v. This may also be viewed as an alternative proof that the obvious necessary conditions for the existence of odd cycle systems are also sufficient.

Rotational k-cycle systems of order v<3k; another proof of the existence of odd cycle systems / Buratti, Marco. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 11:6(2003), pp. 433-441. [10.1002/jcd.10061]

Rotational k-cycle systems of order v<3k; another proof of the existence of odd cycle systems

BURATTI, Marco
2003

Abstract

We give an explicit solution to the existence problem for 1-rotational k-cycle systems of order v < 3k with k odd and v ≠ 2k + 1. We also exhibit a 2-rotational k-cycle system of order 2k + 1 for any odd k. Thus, for k odd and any admissible v < 3k there exists a 2-rotational k-cycle system of order v. This may also be viewed as an alternative proof that the obvious necessary conditions for the existence of odd cycle systems are also sufficient.
2003
sistemi di k-cicli; gruppi di automorfismi
01 Pubblicazione su rivista::01a Articolo in rivista
Rotational k-cycle systems of order v<3k; another proof of the existence of odd cycle systems / Buratti, Marco. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 11:6(2003), pp. 433-441. [10.1002/jcd.10061]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654650
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