I, uh, wasted a bit of time once on the Tree Packing conjecture of Gyarfas: https://arxiv.org/abs/1104.0642 https://arxiv.org/abs/1104.0642 In your left hand,

I, uh, wasted a bit of time once on the Tree Packing conjecture of Gyarfas: https://arxiv.org/abs/1104.0642 https://arxiv.org/abs/1104.0642 In your left hand, place a complete graph, which has n-choose-2 edges. In your right hand, a collection of trees on 2, 3, 4, ..., n-1 vertices, which, by miraculous concidence, also has n-choose-2 edges. Q: Can you pack the trees into a complete graph with no overlapping edges?