Existence of 1-Rotational k-Cycle Systems of the Complete Graph

Abstract.

We explicitly solve the existence problem for 1-rotational k-cycle systems of the complete graph K _v with v≡1 or k (mod 2k). For v≡1 (mod 2k) we have existence if and only if k is an odd composite number. For any odd k and v≡k (mod 2k), (except k≡3 and v≡15, 21 (mod 24)) a 1-rotational k-cycle system of K _v exists.