Planar drawing is preserved by edge removal
ProvedWilliamsonShmoys.hasPlanarDrawingOn_mono__p2m_70f84f17_dac3_4815_92df_56beadc09612_a2approximation-algorithmsplanar-graphstreewidth
A drawing witnessing HasPlanarDrawingOn for a graph also witnesses it for any subgraph on the same vertices.
Preamble
import Definitions.Def_WilliamsonShmoys_PlanarDrawingOn import Mathlib set_option autoImplicit false
Formal statement
theorem WilliamsonShmoys.hasPlanarDrawingOn_mono__p2m_70f84f17_dac3_4815_92df_56beadc09612_a2
{V : Type} [Fintype V] [LinearOrder V]
{G H : SimpleGraph V} (hHG : H ≤ G)
(hG : WilliamsonShmoys.HasPlanarDrawingOn G) :
WilliamsonShmoys.HasPlanarDrawingOn H := 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).