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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.15733 |
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| _version_ | 1866908485864652800 |
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| author | Reed, Bruce Stein, Maya |
| author_facet | Reed, Bruce Stein, Maya |
| contents | The Erdős-Sós Conjecture states that every graph with average degree exceeding $k-1$ contains every tree with $k$ edges as a subgraph. We prove that there are $δ>0$ and $k_0\in\mathbb N$ such that the conjecture holds for every tree $T$ with $k \ge k_0$ edges and every graph $G$ with $|V(G)| \le (1+δ)|V(T)|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15733 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding Nearly Spanning Trees Reed, Bruce Stein, Maya Combinatorics The Erdős-Sós Conjecture states that every graph with average degree exceeding $k-1$ contains every tree with $k$ edges as a subgraph. We prove that there are $δ>0$ and $k_0\in\mathbb N$ such that the conjecture holds for every tree $T$ with $k \ge k_0$ edges and every graph $G$ with $|V(G)| \le (1+δ)|V(T)|$. |
| title | Embedding Nearly Spanning Trees |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.15733 |