It has been noted that there are seven non-isomorphic nontrivial trees of order 5 or

Chapter 13, Problem 28

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It has been noted that there are seven non-isomorphic nontrivial trees of order 5 or less, namely three of size 4, two of size 3, one of size 2 and one of size 1. The sum of the sizes of these seven trees is 21, which is also the size of K7. Do there exist seven such pairwise edge-disjoint trees in K7?

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