Finite maximal drawable supergraph
ProvedWilliamsonShmoys.planar_drawing_has_maximal_extension__p2m_f8b110d8_67db_4582_b9bf_9e52697d207d_a1approximation-algorithmsplanar-graphstreewidth
Every drawable graph on a finite ordered vertex type has a drawable supergraph that is maximal among drawable supergraphs on that same vertex type.
Preamble
import Definitions.Def_WilliamsonShmoys_PlanarDrawingOn set_option autoImplicit false
Formal statement
theorem WilliamsonShmoys.planar_drawing_has_maximal_extension__p2m_f8b110d8_67db_4582_b9bf_9e52697d207d_a1
{V : Type} [Fintype V] [LinearOrder V]
(R : SimpleGraph V) (hR : WilliamsonShmoys.HasPlanarDrawingOn R)
(hcard : 3 ≤ Fintype.card V) :
∃ S : SimpleGraph V, R ≤ S ∧ WilliamsonShmoys.HasPlanarDrawingOn S ∧
∀ T : SimpleGraph V, S ≤ T → WilliamsonShmoys.HasPlanarDrawingOn T → T = S := by sorrySource
David P. Williamson and David B. Shmoys, The Design of Approximation Algorithms, Cambridge University Press, 2011, author electronic manuscript, Section 10.2, proof of Theorem 10.11, pp. 270-272. https://doi.org/10.1017/CBO9780511921735. Bounded tree-width of the pieces: Robertson–Seymour (planar graphs of radius r have tree-width at most 3r+1) / Bodlaender (k-outerplanar graphs have tree-width at most 3k-1).