Refuting Perfect Matchings in Spectral Expanders is Hard
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908827064991744 |
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| author | Biswas, Ari Nenadov, Rajko |
| author_facet | Biswas, Ari Nenadov, Rajko |
| contents | This work studies the complexity of refuting the existence of a perfect matching in spectral expanders with an odd number of vertices, in the Polynomial Calculus (PC) and Sum of Squares (SoS) proof system. Austrin and Risse [SODA, 2021] showed that refuting perfect matchings in sparse $d$-regular \emph{random} graphs, in the above proof systems, with high probability requires proofs with degree $Ω(n/\log n)$. We extend their result by showing the same lower bound holds for \emph{all} $d$-regular graphs with a mild spectral gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refuting Perfect Matchings in Spectral Expanders is Hard Biswas, Ari Nenadov, Rajko Combinatorics Computational Complexity This work studies the complexity of refuting the existence of a perfect matching in spectral expanders with an odd number of vertices, in the Polynomial Calculus (PC) and Sum of Squares (SoS) proof system. Austrin and Risse [SODA, 2021] showed that refuting perfect matchings in sparse $d$-regular \emph{random} graphs, in the above proof systems, with high probability requires proofs with degree $Ω(n/\log n)$. We extend their result by showing the same lower bound holds for \emph{all} $d$-regular graphs with a mild spectral gap. |
| title | Refuting Perfect Matchings in Spectral Expanders is Hard |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2506.07700 |