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
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.File in questo prodotto:
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