Planar drawing restricts to subgraphs
ProvedWilliamsonShmoys.hasPlanarDrawingOn_subgraph__p2m_dbde89e8_c849_4801_a07f_e697f1afc8ec_a1approximation-algorithmsplanar-graphstreewidth
If G is a subgraph of G' on the same ordered vertex type and G' has a crossing-free drawing, then G has one too.
Preamble
import Definitions.Def_WilliamsonShmoys_PlanarDrawingOn set_option autoImplicit false
Formal statement
theorem WilliamsonShmoys.hasPlanarDrawingOn_subgraph__p2m_dbde89e8_c849_4801_a07f_e697f1afc8ec_a1
{V : Type} [Fintype V] [LinearOrder V]
{G G' : SimpleGraph V} (h : G ≤ G')
(hG' : WilliamsonShmoys.HasPlanarDrawingOn G') :
WilliamsonShmoys.HasPlanarDrawingOn G := 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).