Graph Colouring Is Hard on Average for Polynomial Calculus and Nullstellensatz
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866908276893941760 |
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| author | Conneryd, Jonas de Rezende, Susanna F. Nordström, Jakob Pang, Shuo Risse, Kilian |
| author_facet | Conneryd, Jonas de Rezende, Susanna F. Nordström, Jakob Pang, Shuo Risse, Kilian |
| contents | We prove that polynomial calculus (and hence also Nullstellensatz) over any field requires linear degree to refute that sparse random regular graphs, as well as sparse Erdős-Rényi random graphs, are $3$-colourable. Using the known relation between size and degree for polynomial calculus proofs, this implies strongly exponential lower bounds on proof size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph Colouring Is Hard on Average for Polynomial Calculus and Nullstellensatz Conneryd, Jonas de Rezende, Susanna F. Nordström, Jakob Pang, Shuo Risse, Kilian Computational Complexity F.2.2; F.1.3; I.2.3; F.4.1 We prove that polynomial calculus (and hence also Nullstellensatz) over any field requires linear degree to refute that sparse random regular graphs, as well as sparse Erdős-Rényi random graphs, are $3$-colourable. Using the known relation between size and degree for polynomial calculus proofs, this implies strongly exponential lower bounds on proof size. |
| title | Graph Colouring Is Hard on Average for Polynomial Calculus and Nullstellensatz |
| topic | Computational Complexity F.2.2; F.1.3; I.2.3; F.4.1 |
| url | https://arxiv.org/abs/2503.17022 |