Planar drawings are inherited by subgraphs
ProvedWilliamsonShmoys.planarDrawingOn_of_le__p2m_138d462c_20bd_43cc_9c59_565c454fd505_a1approximation-algorithmsplanar-graphstreewidth
If a graph has the specified crossing-free drawing, every subgraph on the same vertices has that drawing too.
Preamble
import Definitions.Def_WilliamsonShmoys_PlanarDrawingOn set_option autoImplicit false
Formal statement
theorem WilliamsonShmoys.planarDrawingOn_of_le__p2m_138d462c_20bd_43cc_9c59_565c454fd505_a1
{V : Type} [Fintype V] [LinearOrder V]
{H K : SimpleGraph V} (hHK : H ≤ K)
(hK : WilliamsonShmoys.HasPlanarDrawingOn K) : 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).