@misc{BeisegelRatajczakScheffler, author = {Beisegel, Jesse and Ratajczak, Fabienne and Scheffler, Robert}, title = {Computing hamiltonian paths with partial order restrictions}, series = {ACM Transactions on Computation Theory}, volume = {17}, journal = {ACM Transactions on Computation Theory}, number = {1}, issn = {1942-3454}, doi = {10.1145/3711844}, pages = {1 -- 24}, abstract = {When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example, one could decide whether a Hamiltonian path exists for a fixed starting point, or that some vertices are visited before another vertex. We consider the problem of finding a Hamiltonian path that observes all precedence constraints given in a partial order on the vertex set. We show that this problem is NP-complete even if restricted to complete bipartite graphs and posets of height 2. In contrast, for posets of width k there is a known O(k^2 n^k) algorithm for arbitrary graphs with n vertices. We show that it is unlikely that the running time of this algorithm can be improved significantly, i.e., there is no f(k) n^o(k) time algorithm under the assumption of the Exponential Time Hypothesis. Furthermore, for the class of outerplanar graphs, we give an O(n^2) algorithm for arbitrary posets.}, language = {en} }