Resolvable 3-star designs

Let Kv be the complete graph of order v and F be a set of 1-factors of Kv. In this article we study the existence of a resolvable decomposition of Kv - F into 3-stars when F has the minimum number of 1-factors. We completely solve the case in which F has the minimum number of 1- factors, with the possible exception of v in {40, 44, 52, 76, 92, 100, 280, 284, 328, 332, 428, 472, 476, 572}.