Counting big Ramsey degrees of the homogeneous and universal $K_4$-free graph
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915523538714624 |
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| author | Hubička, Jan Konečný, Matěj Vodseďálek, Štěpán Zucker, Andy |
| author_facet | Hubička, Jan Konečný, Matěj Vodseďálek, Štěpán Zucker, Andy |
| contents | Big Ramsey degrees of Fraïssé limits of finitely constrained free amalgamation classes in finite binary languages have been recently fully characterised by Balko, Chodounský, Dobrinen, Hubička, Konečný, Vena, and Zucker. A special case of this characterisation is the universal homogeneous $K_4$-free graph. We give a self-contained and relatively compact presentation of this case and compute the actual big Ramsey degrees of small graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting big Ramsey degrees of the homogeneous and universal $K_4$-free graph Hubička, Jan Konečný, Matěj Vodseďálek, Štěpán Zucker, Andy Combinatorics Discrete Mathematics Logic 05C55, 05D10, 05C30 G.2.1; G.2.2 Big Ramsey degrees of Fraïssé limits of finitely constrained free amalgamation classes in finite binary languages have been recently fully characterised by Balko, Chodounský, Dobrinen, Hubička, Konečný, Vena, and Zucker. A special case of this characterisation is the universal homogeneous $K_4$-free graph. We give a self-contained and relatively compact presentation of this case and compute the actual big Ramsey degrees of small graphs. |
| title | Counting big Ramsey degrees of the homogeneous and universal $K_4$-free graph |
| topic | Combinatorics Discrete Mathematics Logic 05C55, 05D10, 05C30 G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2505.22620 |