We explicitly solve the existence problem for 1-rotational k-cycle systems of the complete graph $K_v$ with $v \equiv 1$ or k (mod 2k). For $v \equiv 1$ (mod 2k) we have existence if and only if k is an odd composite number. For any odd k and $v \equiv k$ (mod 2k), (except k = 3 and $v \equiv 15, 21$ (mod 24)) a 1-rotational k-cycle system of $K_v$ exists.
Existence of 1-rotational k-cycle systems of the complete graph
BURATTI, Marco
2004
Abstract
We explicitly solve the existence problem for 1-rotational k-cycle systems of the complete graph $K_v$ with $v \equiv 1$ or k (mod 2k). For $v \equiv 1$ (mod 2k) we have existence if and only if k is an odd composite number. For any odd k and $v \equiv k$ (mod 2k), (except k = 3 and $v \equiv 15, 21$ (mod 24)) a 1-rotational k-cycle system of $K_v$ exists.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
