Retractions onto series-parallel posets

The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable, and, for such a poset P, we describe posets admitting a retraction onto P.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Víctor Dalmau, Andrei A. Krokhin, Benoit Larose
• Keywords: DM 2008, Poset Retraction Problem, Retraction, Series-parallel Posets