On Turán-type problems and the abstract chromatic number
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914970582646784 |
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| author | Gerbner, Dániel Karim, Hilal Hama Kucheriya, Gaurav |
| author_facet | Gerbner, Dániel Karim, Hilal Hama Kucheriya, Gaurav |
| contents | In 2020, Coregliano and Razborov introduced a general framework to study limits of combinatorial objects, using logic and model theory. They introduced the abstract chromatic number and proved/reproved multiple Erdős-Stone-Simonovits-type theorems in different settings. In 2022, Coregliano extended this by showing that similar results hold when we count copies of $K_t$ instead of edges.
Our aim is threefold. First, we provide a purely combinatorial approach. Second, we extend their results by showing several other graph parameters and other settings where Erdős-Stone-Simonovits-type theorems follow. Third, we go beyond determining asymptotics and obtain corresponding stability, supersaturation, and sometimes even exact results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Turán-type problems and the abstract chromatic number Gerbner, Dániel Karim, Hilal Hama Kucheriya, Gaurav Combinatorics 05C35 In 2020, Coregliano and Razborov introduced a general framework to study limits of combinatorial objects, using logic and model theory. They introduced the abstract chromatic number and proved/reproved multiple Erdős-Stone-Simonovits-type theorems in different settings. In 2022, Coregliano extended this by showing that similar results hold when we count copies of $K_t$ instead of edges. Our aim is threefold. First, we provide a purely combinatorial approach. Second, we extend their results by showing several other graph parameters and other settings where Erdős-Stone-Simonovits-type theorems follow. Third, we go beyond determining asymptotics and obtain corresponding stability, supersaturation, and sometimes even exact results. |
| title | On Turán-type problems and the abstract chromatic number |
| topic | Combinatorics 05C35 |
| url | https://arxiv.org/abs/2410.09617 |