Resolvable 3-star designs

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