Let T_1,…,T_n be trees such that T_k has k vertices for every k with 1≤ k≤ n, and let K_n be the complete graph on n vertices. Gyárfás's tree-packing conjecture. The trees T_1,…,T_n pack into K_n. The paper presents this as the conjecture it proves, so it is resolved by the source's claimed result.

Gyárfás's tree-packing conjecture

Let $T_1,\ldots,T_n$ be trees such that $T_k$ has $k$ vertices for every $k$ with $1\leq k\leq n$ , and let $K_n$ be the complete graph on $n$ vertices. Gyárfás's tree-packing conjecture. The trees $T_1,\ldots,T_n$ pack into $K_n$ . The paper presents this as the conjecture it proves, so it is resolved by the source's claimed result.

Sources & referencesView supporting material

Primary source

Parikshit Chalise, Antwan Clark and Edinah K. Gnang, “A Proof of the Tree Packing Conjecture”, arXiv:2410.13840 (2024).

Additional references

12 papers in this index state this conjecture (2011–2024). The statement above is taken from the most recent of them; the others are arXiv:2410.13290, arXiv:2109.04900, arXiv:2105.07038, arXiv:1803.03316, arXiv:1602.06780, arXiv:1510.05190, arXiv:1509.05539, arXiv:1407.5083, arXiv:1404.0697, arXiv:1205.5492, arXiv:1104.0642.

Source: https://arxiv.org/abs/2410.13840 Gyárfás (1976), cited in the source

graph-decomposition tree-packing

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