On Complexity of Some Chain and Antichain Partition Problems

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