Finiteness of simple graphs on a finite vertex type
ProvedWilliamsonShmoys.finite_simpleGraph__p2m_16fb1a0d_e68c_4595_a206_2f4554b0589b_a2approximation-algorithmsplanar-graphstreewidth
For a finite linearly ordered vertex type, the type of simple graphs on it is finite.
Preamble
import Mathlib open SimpleGraph
Formal statement
theorem WilliamsonShmoys.finite_simpleGraph__p2m_16fb1a0d_e68c_4595_a206_2f4554b0589b_a2
{V : Type} [Fintype V] [LinearOrder 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).