Infinitely many minimally non-Ramsey size-linear graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909600432783360 |
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| author | Wigderson, Yuval |
| author_facet | Wigderson, Yuval |
| contents | A graph $G$ is said to be Ramsey size-linear if $r(G,H) =O_G (e(H))$ for every graph $H$ with no isolated vertices. Erdős, Faudree, Rousseau, and Schelp observed that $K_4$ is not Ramsey size-linear, but each of its proper subgraphs is, and they asked whether there exist infinitely many such graphs. In this short note, we answer this question in the affirmative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinitely many minimally non-Ramsey size-linear graphs Wigderson, Yuval Combinatorics A graph $G$ is said to be Ramsey size-linear if $r(G,H) =O_G (e(H))$ for every graph $H$ with no isolated vertices. Erdős, Faudree, Rousseau, and Schelp observed that $K_4$ is not Ramsey size-linear, but each of its proper subgraphs is, and they asked whether there exist infinitely many such graphs. In this short note, we answer this question in the affirmative. |
| title | Infinitely many minimally non-Ramsey size-linear graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.05931 |