Monotonicity of finite graph edge counts
ProvedSimpleGraph.edgeSet_ncard_mono__p2m_62578b33_7986_4643_ae9c_c0cb30164949_a1approximation-algorithmsplanar-graphstreewidth
On a finite vertex type, inclusion of simple graphs implies monotonicity of the cardinality of their edge sets.
Preamble
import Mathlib set_option autoImplicit false
Formal statement
theorem SimpleGraph.edgeSet_ncard_mono__p2m_62578b33_7986_4643_ae9c_c0cb30164949_a1
{V : Type} [Fintype V] (G H : SimpleGraph V) (h : G ≤ H) :
G.edgeSet.ncard ≤ H.edgeSet.ncard := 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).