Embedding clique subdivisions via crux
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909210022772736 |
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| author | Yang, Donglei Yang, Fan |
| author_facet | Yang, Donglei Yang, Fan |
| contents | For a graph $G$ and a constant $α>0$, we denote by $C_α(G)$ the minimum order of a subgraph $H\subseteq G$ with $d(H)\ge αd(G)$. Liu and Montgomery conjectured that every graph $G$ contains $K_{Ω(t)}$ as a subdivision for $t=\min \{d(G), \sqrt{\tfrac{C_α(G)}{\log C_α(G)}}\}$. In the paper, we prove this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding clique subdivisions via crux Yang, Donglei Yang, Fan Combinatorics For a graph $G$ and a constant $α>0$, we denote by $C_α(G)$ the minimum order of a subgraph $H\subseteq G$ with $d(H)\ge αd(G)$. Liu and Montgomery conjectured that every graph $G$ contains $K_{Ω(t)}$ as a subdivision for $t=\min \{d(G), \sqrt{\tfrac{C_α(G)}{\log C_α(G)}}\}$. In the paper, we prove this conjecture. |
| title | Embedding clique subdivisions via crux |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.15409 |