A Proof of the Tree Packing Conjecture
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910662502907904 |
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| author | Chalise, Parikshit Clark, Antwan Gnang, Edinah K. |
| author_facet | Chalise, Parikshit Clark, Antwan Gnang, Edinah K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Proof of the Tree Packing Conjecture Chalise, Parikshit Clark, Antwan Gnang, Edinah K. Combinatorics 05C70, 05B30 G.2.2 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. |
| title | A Proof of the Tree Packing Conjecture |
| topic | Combinatorics 05C70, 05B30 G.2.2 |
| url | https://arxiv.org/abs/2410.13840 |