Planar drawing is preserved under taking subgraphs
ProvedWilliamsonShmoys_hasPlanarDrawingOn_mono__p2m_f3863ecb_d96f_4f01_8e13_caf8f4700d63_a2approximation-algorithmsplanar-graphstreewidth
A drawing of a graph also draws each of its subgraphs on the same vertex type, by reusing its vertex positions and edge arcs.
Preamble
import Definitions.Def_WilliamsonShmoys_PlanarDrawingOn import Mathlib set_option autoImplicit false
Formal statement
theorem WilliamsonShmoys_hasPlanarDrawingOn_mono__p2m_f3863ecb_d96f_4f01_8e13_caf8f4700d63_a2
{V : Type} [Fintype V] [LinearOrder V]
{G H : SimpleGraph V} (hGH : G ≤ H)
(hH : WilliamsonShmoys.HasPlanarDrawingOn H) :
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).