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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.07147 |
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| _version_ | 1866918050318516224 |
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| author | Sun, Wanting Wei, Shunan Yang, Donglei |
| author_facet | Sun, Wanting Wei, Shunan Yang, Donglei |
| contents | We prove that for all $μ>0, t\in (0,1)$ and sufficiently large $n\in 4\mathbb{N}$, if $G$ is an edge-weighted complete graph on $n$ vertices with a weight function $w: E(G)\rightarrow [0,1]$ and the minimum weighted degree $δ^w(G)\geq (\tfrac{1+3t}{4}+μ)n$, then $G$ contains a $K_4$-factor where each copy of $K_4$ has total weight more than $6t$. This confirms a conjecture of Balogh--Kemkes--Lee--Young for the tetrahedron case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Packing tetrahedrons in edge-weighted graphs Sun, Wanting Wei, Shunan Yang, Donglei Combinatorics We prove that for all $μ>0, t\in (0,1)$ and sufficiently large $n\in 4\mathbb{N}$, if $G$ is an edge-weighted complete graph on $n$ vertices with a weight function $w: E(G)\rightarrow [0,1]$ and the minimum weighted degree $δ^w(G)\geq (\tfrac{1+3t}{4}+μ)n$, then $G$ contains a $K_4$-factor where each copy of $K_4$ has total weight more than $6t$. This confirms a conjecture of Balogh--Kemkes--Lee--Young for the tetrahedron case. |
| title | Packing tetrahedrons in edge-weighted graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.07147 |