Catalog/Sparsity/UQWEquivND/Contract.lean
| 1 | import Catalog.Sparsity.Preliminaries.Contract |
| 2 | import Catalog.Sparsity.NowhereDense.Contract |
| 3 | import Catalog.Sparsity.UniformQuasiWideness.Contract |
| 4 | |
| 5 | namespace Catalog.Sparsity.UQWEquivND |
| 6 | |
| 7 | open Catalog.Sparsity.Preliminaries Catalog.Sparsity.NowhereDense Catalog.Sparsity.UniformQuasiWideness |
| 8 | |
| 9 | /-- Theorem 3.2: a class of graphs is uniformly quasi-wide if and only if it is |
| 10 | nowhere dense. -/ |
| 11 | axiom uqw_iff_nd (C : GraphClass) : |
| 12 | UniformlyQuasiWide C ↔ IsNowhereDense C |
| 13 | |
| 14 | end Catalog.Sparsity.UQWEquivND |
| 15 |