%0 Journal Article
%T All Permutations Supersequence is coNP-complete
%A Przemys£¿aw Uzna¨½ski
%J Computer Science
%D 2015
%I arXiv
%X We prove that deciding whether a given input word contains as subsequence every possible permutation of integers $\{1,2,\ldots,n\}$ is coNP-complete. The coNP-completeness holds even when given the guarantee that the input word contains as subsequences all of length $n-1$ sequences over the same set of integers. We also show NP-completeness of a related problem of Partially Non-crossing Perfect Matching in Bipartite Graphs, i.e. to find a perfect matching in an ordered bipartite graph where edges of the matching incident to selected vertices (even only from one side) are non-crossing.
%U http://arxiv.org/abs/1506.05079v2