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Given a graph $G$, the NP-hard Maximum Planar Subgraph problem asks for aplanar subgraph of $G$ with the maximum number of edges. The only knownnon-trivial exact algorithm utilizes Kuratowski's famous planarity criterionand can be formulated as an integer linear program (ILP) or a pseudo-booleansatisfiability problem (PBS). We examine three alternative characterizations ofplanarity regarding their applicability to model maximum planar subgraphs. Foreach, we consider both ILP and PBS variants, investigate diverse formulationaspects, and evaluate their practical performance.

Exact Algorithms for the Maximum Planar Subgraph Problem: New Models and Experiments