E. Cheng, L.-H. Hsu, C.-N. Hung, M.-C. Yang
2-spanning cyclability problems of the some generalized Petersen graphs
Discussiones Mathematicae Graph Theory
Received 18.09.2017, Revised 05.03.2018, Accepted 05.03.2018, doi: 10.7151/dmgt.2150
A graph G is called r-spanning cyclable if for every r distinct vertices v1,v2,...,vr of G, there exists r cycles C1,C2,..., Cr in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci. In this paper, we consider the 2-spanning cyclable problem for the generalized Petersen graph GP(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.
Petersen graph, spanning cyclable