Spanning clique subdivisions in pseudorandom graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915223376494592 |
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| author | Lee, Hyunwoo Pavez-Signé, Matías Petrov, Teo |
| author_facet | Lee, Hyunwoo Pavez-Signé, Matías Petrov, Teo |
| contents | In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following three results. Firstly, that there are constants $C>0$ and $c\in (0,1]$ such that, whenever $d/λ\ge C$, every $(n,d,λ)$-graph contains a spanning subdivision of $K_t$ for all $2\le t \le \min\{cd,c\sqrt{\frac{n}{\log n}}\}$. Secondly, that there are constants $C>0$ and $c\in (0,1]$ such that, whenever $d/λ\ge C\log^3n$, every $(n,d,λ)$-graph contains a spanning nearly-balanced subdivision of $K_t$ for all $2\le t \le \min\{cd,c\sqrt{\frac{n}{\log^3n}}\}$. Finally, we show that for every $μ>0$, there are constants $c,\varepsilon\in (0,1]$ and $n_0\in \mathbb N$ such that, whenever $n\ge n_0$, every $n$-vertex graph with minimum degree at least $μn$ and no bipartite holes of size $\varepsilon n$ contains a spanning nearly-balanced subdivision of $K_t$ for all $2\le t \le c\sqrt{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spanning clique subdivisions in pseudorandom graphs Lee, Hyunwoo Pavez-Signé, Matías Petrov, Teo Combinatorics In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following three results. Firstly, that there are constants $C>0$ and $c\in (0,1]$ such that, whenever $d/λ\ge C$, every $(n,d,λ)$-graph contains a spanning subdivision of $K_t$ for all $2\le t \le \min\{cd,c\sqrt{\frac{n}{\log n}}\}$. Secondly, that there are constants $C>0$ and $c\in (0,1]$ such that, whenever $d/λ\ge C\log^3n$, every $(n,d,λ)$-graph contains a spanning nearly-balanced subdivision of $K_t$ for all $2\le t \le \min\{cd,c\sqrt{\frac{n}{\log^3n}}\}$. Finally, we show that for every $μ>0$, there are constants $c,\varepsilon\in (0,1]$ and $n_0\in \mathbb N$ such that, whenever $n\ge n_0$, every $n$-vertex graph with minimum degree at least $μn$ and no bipartite holes of size $\varepsilon n$ contains a spanning nearly-balanced subdivision of $K_t$ for all $2\le t \le c\sqrt{n}$. |
| title | Spanning clique subdivisions in pseudorandom graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.01642 |