2-spanning cyclability problems of the some generalized Petersen graphs

A graph G is called r-spanning cyclable if for every r distinct vertices v(1),v(2), ...,v(r) of G, there exists r cycles C-1,C-2, ...,C-r in G such that v(i) is on C-i for every i, and every vertex of G is on exactly one cycle C-i. In this paper, we consider the 2-spanning cyclable problem for the generalized Petersen graph G P (n, k). We solved the problem for k <= 4. In addition, we provide an additional observation for general k as well as stating a conjecture.