On complexity of some chain and antichain partition problems

Abstract

In the paper we deal with computational complexity of a problem Ck (respectively Ak) of a partition of an ordered set into minimum number of at most k-element chains (resp. antichains). We show that Ck, k ≥ 3, is NP-complete even for N-free ordered sets of length at most k, Ck and Ak are polynomial for series-paralel orders and Ak is polynomial for interval orders. We also consider related problems for graphs.