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

About 2 years old · traced to 2024

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.

References

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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