Retractions onto series-parallel posets

Dalmau, Víctor; Krokhin, Andrei; Larose, Benoit

doi:http://dx.doi.org/10.1016/j.disc.2006.08.010

Retractions onto series-parallel posets

Citation

Dalmau V, Krokhin A, Larose B. Retractions onto series-parallel posets. Discrete Math. 2008 Jun 6;308(11):2104-14. DOI: 10.1016/j.disc.2006.08.010

Abstract

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 . 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.