Jiménez, AndreaAndreaJiménezSchmidt, Tina JanneTina JanneSchmidt2020-01-032020-01-032019Electronic Notes in Theoretical Computer Science (346): 545-556 (2019)http://hdl.handle.net/11420/4252The Topological Subgraph Containment (TSC) Problem is to decide, for two given graphs G and H, whether H is a topological subgraph of G. It is known that the TSC Problem is NP-complete when H is part of the input, that it can be solved in polynomial time when H is fixed, and that it is fixed-parameter tractable by the order of H. Motivated by the great significance of grids in graph theory and algorithms due to the Grid-Minor Theorem by Robertson and Seymour, we investigate the computational complexity of the Grid TSC Problem in planar graphs. More precisely, we study the following decision problem: given a positive integer k and a planar graph G, is the k × k grid a topological subgraph of G? We prove that this problem is NP-complete, even when restricted to planar graphs of maximum degree six, via a novel reduction from the Planar Monotone 3-SAT Problem.en1571-06612019545556Elsevierhttps://creativecommons.org/licenses/by-nc-nd/4.0/gridsNP-completeplanar graphsubdivisionsubgraph homeomorphismtopological subgraphMathematikConference Paper10.15480/882.255210.1016/j.entcs.2019.08.04810.15480/882.2552Conference Paper