| A k-regular graph is called panfactorical, or even panfactorical respectively,if for every integer s, 1 ≤ s ≤ k,there exists an s-factor, or 2[s/2]-factor, in this graph.A criterion for checking an r-regular graph to be panfactorical or even panfactorical isestablished. It is proved that every Cayley graph of odd degree is panfactorical and everyCayley graph of even degree is even panfactorical by using this criterion. For a dihedralgroup, we prove that every connected Cayley graph on this group is panfactorial. |
