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Abstract:We prove a conjecture of Gyárfás (1976), which asserts that any family of trees $T_1, \dots, T_{n}$ where each $T_k$ has $k$ vertices packs into $K_n$. We do so by translating the decomposition problem into a labeling problem, namely complete labeling. Our proof employs the polynomial method using a functional reformulation of the conjecture.
From: Parikshit Chalise [view email]
[v1]
Thu, 17 Oct 2024 17:56:12 UTC (17 KB)
[v2]
Wed, 23 Oct 2024 15:29:44 UTC (17 KB)
[v3]
Tue, 1 Sep 2026 21:48:44 UTC (1 KB) (withdrawn)
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