Packing trees in complete graphs (Q1101132)

Trees \(T_ 1,T_ 2,...,T_ k\) are said to pack into \(K_ n\) if the edge-set of \(K_ n\) can be partitioned into \(k+1\) subgraphs of which k are isomorphic to \(T_ 1,T_ 2,...,T_ k\). A number of results are proved about when such packings are possible. For example, three trees of different orders can be thus packed, as can a set \(T_ 2,T_ 3,...,T_ n\) when each \(T_ i\) has order i and at most one \(T_ i\) has diameter greater than three.