The Oberwolfach problem for a unique 5-cycle and all others of length 3

Abstract

In this paper it is proved that, for any positive integer n ≡ 5 (mod 6), n ≥ 5 and n ≠ 11, there exists an Oberwolfach problem with all cycles to be of length three except that each 2-factor contains one cycle of length five. This result provides an application to the number of triangles in 2-factorizations.