A special case of the tree packing conjecture

Gubanyi, Marcus E (Concordia University Nebraska)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications

The Tree Packing Conjecture of Gyárfás states that for any set of n-1 trees T = {T₁, T₂, …, Tn-1}, where Ti has i edges, T can be packed into Kn. We define a family of trees called two-spiders that are almost stars, and show that packings of Kn with two-spiders can be constructed by exchanging edges of known packings. We prove that if each tree Ti ∈ T is a two-spider and has at most α i two-legs for α = (3-√5)/4, then T packs into Kn.