The problem of deciding whether a biconnected planar digraph G=(V,E) can be augmented to become an st-planar graph by adding a set of oriented edges E′⊆V×V is known to be NP-complete. We show that the problem is fixed-parameter tractable when parameterized by the size of the set E′.
@article{arxiv.2309.15454,
title = {The $st$-Planar Edge Completion Problem is Fixed-Parameter Tractable},
author = {Liana Khazaliya and Philipp Kindermann and Giuseppe Liotta and Fabrizio Montecchiani and Kirill Simonov},
journal= {arXiv preprint arXiv:2309.15454},
year = {2023}
}