Crowns as retracts
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866918012347482112 |
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| author | Campo, Frank a |
| author_facet | Campo, Frank a |
| contents | We investigate crowns as retracts of finite posets. We define a multigraph $\mathfrak{F}(P)$ reflecting the network of so-called improper 4-crowns contained in the extremal points of $P$, and we show that $P$ contains a 4-crown as retract iff there exists a graph homomorphism of a certain type from $\mathfrak{F}(P)$ to a multigraph $\mathfrak{C}$ not depending on $P$. Additionally we show that $P$ contains a retract-crown with more than four points iff the poset induced by the extremal points of $P$ contains such a retract-crown. As practical result we develop and apply criteria for the systematic investigation of crowns as retracts. Most of our results are valid for infinite posets without infinite chains, too. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_09588 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Crowns as retracts Campo, Frank a Combinatorics 06A07 (Primary) 06A06 (Secondary) We investigate crowns as retracts of finite posets. We define a multigraph $\mathfrak{F}(P)$ reflecting the network of so-called improper 4-crowns contained in the extremal points of $P$, and we show that $P$ contains a 4-crown as retract iff there exists a graph homomorphism of a certain type from $\mathfrak{F}(P)$ to a multigraph $\mathfrak{C}$ not depending on $P$. Additionally we show that $P$ contains a retract-crown with more than four points iff the poset induced by the extremal points of $P$ contains such a retract-crown. As practical result we develop and apply criteria for the systematic investigation of crowns as retracts. Most of our results are valid for infinite posets without infinite chains, too. |
| title | Crowns as retracts |
| topic | Combinatorics 06A07 (Primary) 06A06 (Secondary) |
| url | https://arxiv.org/abs/2111.09588 |