
arXiv: 2111.09588
Abstract We characterize finite, connected posets $P$ having a crown as retract. We define a multigraph $\mathfrak{F}(P)$ whose vertices are the 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 $n \geq 6$ points iff the poset induced by the extremal points of $P$ contains a retract-crown with $n$ points.Mathematics Subject Classification: Primary: 06A07. Secondary: 06A06.
06A07 (Primary) 06A06 (Secondary), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
06A07 (Primary) 06A06 (Secondary), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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