Theorems · Theorem · combinatorics
SimpleGraph.not_isTutteViolator_of_isPerfectMatching
∀ {V : Type u_1} {G : SimpleGraph V} [Finite V] {M : G.Subgraph},
M.IsPerfectMatching → ∀ (u : Set V), ¬G.IsTutteViolator uProves the necessity part of Tutte's theorem
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Tutte
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topproof · cited by 9,680
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Finitestatement and proof · cited by 3,029
- SimpleGraph.Subgraphstatement and proof · cited by 326
- Subtype.val_injectiveproof · cited by 232
- SimpleGraph.Subgraph.vertsproof · cited by 210
- SimpleGraph.Subgraph.Adjproof · cited by 147
- SimpleGraph.Subgraph.coeproof · cited by 89
- SimpleGraph.ConnectedComponent.suppproof · cited by 42
- Nat.card_le_card_of_injectiveproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.tutteproof · cited by 0