Packing and Covering of the Complete Graph, IV: The Trees of Order Seven

It is shown that the maximal number of pairwise edge disjoint trees of order seven in the complete graph \(K_n\), and the minimum number of trees of order seven, whose union is \(K_n\), are \(\left\lfloor\frac{n(n-1)}{12}\right\rfloor\) and \(\left\lceil\frac{n(n-1)}{12}\right\rceil,n\geq 11\), respectively. (\(\lfloor x\rfloor\) denotes the largest integer not exceeding \(x\) and \(\lceil x\rceil\) the least integer not less than \(x\)).