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Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast Chimani, Markus Wiedera, Tilo algorithm engineering graph algorithms integer linear programming maximum planar subgraph The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph H of a given graph G such that H has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear programming and Kuratowski's famous planarity criterion. We build upon this approach and present new constraint classes - together with a lifting of the polyhedron - to obtain provably stronger LP-relaxations, and in turn faster algorithms in practice. The new constraints take Euler's polyhedron formula as a starting point and combine it with considering cycles in G. This paper discusses both the theoretical as well as the practical sides of this strengthening. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Markus Chimani and Tilo Wiedera 2018 Is Part Of LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2018.19 urn:nbn:de:0030-drops-94829 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.19 eng https://creativecommons.org/licenses/by/3.0/legalcode