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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Gubanyi, Marcus E
Concordia University Nebraska
Electrical & Electronics Engineering

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A special case of the tree packing conjecture Gubanyi, Marcus E
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.1.11

Abstract

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.
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