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Deciding Whether a Grid is a Topological Subgraph of a Planar Graph is NP-Complete
Citation Link: https://doi.org/10.15480/882.2552
Publikationstyp
Conference Paper
Publikationsdatum
2019
Sprache
English
Institut
TORE-URI
Enthalten in
Volume
346
Start Page
545
End Page
556
Citation
Electronic Notes in Theoretical Computer Science (346): 545-556 (2019)
Contribution to Conference
Publisher DOI
Scopus ID
Publisher
Elsevier
The 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.
Schlagworte
grids
NP-complete
planar graph
subdivision
subgraph homeomorphism
topological subgraph
DDC Class
510: Mathematik
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