Simple graphs on a finite vertex type form a finite type
Provedfinite_simpleGraph_type__p2m_06511e8e_1279_4bc2_b7ef_97610e0642c8_a1approximation-algorithmsplanar-graphstreewidth
There are only finitely many simple graphs on a finite vertex type.
Preamble
import Mathlib set_option autoImplicit false
Formal statement
theorem finite_simpleGraph_type__p2m_06511e8e_1279_4bc2_b7ef_97610e0642c8_a1
{V : Type} [Fintype V] : Finite (SimpleGraph V) := 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).