Resolvable 3-star designs

Let K v be the complete graph of order v and F be a set of 1-factors of K v . In this article we study the existence of a resolvable decomposition of K v - 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 ? { 40 , 44 , 52 , 76 , 92 , 100 , 280 , 284 , 328 , 332 , 428 , 472 , 476 , 572 } .

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