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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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Table of 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.