A Generalization of a Theorem of Erné about the Number of Posets with a Fixed Antichain

Frank a Campo
2021 Order  
We characterize finite, connected posets P having a 4-crown as retract. We define a multigraph 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 𝔉(P) to a multigraph ℭ not depending on P.
doi:10.1007/s11083-021-09585-0 fatcat:hnxd4b5kxnab7p4556k7aa5bwq