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 \(x\)).
Citation
Y. Roditty. Packing and Covering of the Complete Graph, IV: The Trees of Order Seven[J], Ars Combinatoria, Volume 035. 33-64. .