Minimum degree and sparse connected spanning subgraphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911038628167680 |
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| author | Huang, Ting Zhang, Yanbo Chen, Yaojun |
| author_facet | Huang, Ting Zhang, Yanbo Chen, Yaojun |
| contents | Let $G$ be a connected graph on $n$ vertices and at most $n(1+ε)$ edges with bounded maximum degree, and $F$ a graph on $n$ vertices with minimum degree at least $n-k$, where $ε$ is a constant depending on $k$. In this paper, we prove that $F$ contains $G$ as a spanning subgraph provided $n\ge 6k^3$, by establishing tight bounds for the Ramsey number $r(G,K_{1,k})$, where $K_{1,k}$ is a star on $k+1$ vertices. Our result generalizes and refines the work of Erdős, Faudree, Rousseau, and Schelp (JCT-B, 1982), who established the corresponding result for $G$ being a tree. Moreover, the tight bound for $r(G,tK_{1,k})$ is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimum degree and sparse connected spanning subgraphs Huang, Ting Zhang, Yanbo Chen, Yaojun Combinatorics Let $G$ be a connected graph on $n$ vertices and at most $n(1+ε)$ edges with bounded maximum degree, and $F$ a graph on $n$ vertices with minimum degree at least $n-k$, where $ε$ is a constant depending on $k$. In this paper, we prove that $F$ contains $G$ as a spanning subgraph provided $n\ge 6k^3$, by establishing tight bounds for the Ramsey number $r(G,K_{1,k})$, where $K_{1,k}$ is a star on $k+1$ vertices. Our result generalizes and refines the work of Erdős, Faudree, Rousseau, and Schelp (JCT-B, 1982), who established the corresponding result for $G$ being a tree. Moreover, the tight bound for $r(G,tK_{1,k})$ is also obtained. |
| title | Minimum degree and sparse connected spanning subgraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.03264 |