Testing gap k-planarity is NP-complete
JC Urschel, J Wellens - Information Processing Letters, 2021 - Elsevier
For all k≥ 1, we show that deciding whether a graph is k-planar is NP-complete, extending
the well-known fact that deciding 1-planarity is NP-complete. Furthermore, we show that the
gap version of this decision problem is NP-complete. In particular, given a graph with local
crossing number either at most k≥ 1 or at least 2k, we show that it is NP-complete to decide
whether the local crossing number is at most k or at least 2k. This algorithmic lower bound
proves the non-existence of a (2− ϵ)-approximation algorithm for any fixed k≥ 1. In addition …
the well-known fact that deciding 1-planarity is NP-complete. Furthermore, we show that the
gap version of this decision problem is NP-complete. In particular, given a graph with local
crossing number either at most k≥ 1 or at least 2k, we show that it is NP-complete to decide
whether the local crossing number is at most k or at least 2k. This algorithmic lower bound
proves the non-existence of a (2− ϵ)-approximation algorithm for any fixed k≥ 1. In addition …
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