Finding blowups one vertex at a time
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918518173204480 |
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| author | Fox, Jacob Wigderson, Yuval Zhou, Yunkun |
| author_facet | Fox, Jacob Wigderson, Yuval Zhou, Yunkun |
| contents | An influential theorem of Nikiforov states that if an $N$-vertex graph $G$ contains at least $γN^h$ copies of some fixed $h$-vertex graph $H$, then $G$ contains an $H$-blowup of order $c_H(γ)\log N$. We provide a new proof of this theorem, which in particular improves the best known bound on the constant $c_H(γ)$. In contrast to previous proofs, our proof is iterative, finding the blowup one vertex at a time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finding blowups one vertex at a time Fox, Jacob Wigderson, Yuval Zhou, Yunkun Combinatorics An influential theorem of Nikiforov states that if an $N$-vertex graph $G$ contains at least $γN^h$ copies of some fixed $h$-vertex graph $H$, then $G$ contains an $H$-blowup of order $c_H(γ)\log N$. We provide a new proof of this theorem, which in particular improves the best known bound on the constant $c_H(γ)$. In contrast to previous proofs, our proof is iterative, finding the blowup one vertex at a time. |
| title | Finding blowups one vertex at a time |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.23301 |