An update on multicolor Ramsey lower bounds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917215901581312 |
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| author | Campos, Marcelo Pohoata, Cosmin |
| author_facet | Campos, Marcelo Pohoata, Cosmin |
| contents | Building upon previous works by Conlon-Ferber and Wigderson, Sawin showed a few years ago that upper bounds on the minimum density of independent sets in a $K_t$-free $G$ can be used to provide lower bounds for multicolor Ramsey numbers.
In this note, we observe how a further improved upper bound on this parameter directly follows from a recent spherical random geometric graph construction of Ma-Shen-Xie. As a consequence, we derive a small exponential improvement over the best known lower bounds for multicolor Ramsey numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15183 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An update on multicolor Ramsey lower bounds Campos, Marcelo Pohoata, Cosmin Combinatorics Building upon previous works by Conlon-Ferber and Wigderson, Sawin showed a few years ago that upper bounds on the minimum density of independent sets in a $K_t$-free $G$ can be used to provide lower bounds for multicolor Ramsey numbers. In this note, we observe how a further improved upper bound on this parameter directly follows from a recent spherical random geometric graph construction of Ma-Shen-Xie. As a consequence, we derive a small exponential improvement over the best known lower bounds for multicolor Ramsey numbers. |
| title | An update on multicolor Ramsey lower bounds |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.15183 |