On the oberwolfach problem OP(3a, sb) - Cao H.; Mi X. (Utilitas Mathematica, 2011)
The problem of determining whether Kn(for n odd) or K n minus a 1-factor (for n even) has a H-factorization isknown as the Oberwolfach problem.The notation OP(mα11,m α22,⋯,mαtt) represents the case in which each 2-factor must consist of exactly αi mi-cycles for i = 1,2,⋯, t.In this paper, we shall mainly prove that the necessary condition for the existence of 0P(3a,sb) with 1 < b < 3 and s = 4,5 is also sufficient with one exception.