A special case of the tree packing conjecture
Marcus E Gubanyi (marcus.gubanyi@cune.edu)
The Tree Packing Conjecture of Gyárfás states that for any set of n-1 trees T = {T₁, T₂, …, T n-1 }, where T i has i edges, T can be packed into K n . We define a family of trees called two-spiders that are almost stars, and show that packings of K n with two-spiders can be constructed by exchanging edges of known packings. We prove that if each tree T i ∈ T is a two-spider and has at most α i two-legs for α = (3-√5)/4, then T packs into K n .