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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05604 |
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| _version_ | 1866911791786754048 |
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| author | Sands, Bill |
| author_facet | Sands, Bill |
| contents | For each finite poset $F$ with $|F| > 1$, $χ_{ac}(F)$ denotes the smallest integer $n$ (if it exists) such that the elements of every finite poset $P$ with $|P| > 1$ can be coloured with at most $n$ colours so that every maximal $F$-free subset of $P$ with more than one element gets at least two colours. In this note we discuss the problem of determining $χ_{ac}(F)$ for each poset $F$, give one new result, and summarize what is known for posets $F$ with at most four elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Colouring of Maximal $F$-free Subsets Sands, Bill Combinatorics 06 For each finite poset $F$ with $|F| > 1$, $χ_{ac}(F)$ denotes the smallest integer $n$ (if it exists) such that the elements of every finite poset $P$ with $|P| > 1$ can be coloured with at most $n$ colours so that every maximal $F$-free subset of $P$ with more than one element gets at least two colours. In this note we discuss the problem of determining $χ_{ac}(F)$ for each poset $F$, give one new result, and summarize what is known for posets $F$ with at most four elements. |
| title | Colouring of Maximal $F$-free Subsets |
| topic | Combinatorics 06 |
| url | https://arxiv.org/abs/2403.05604 |