Theorems · Theorem · combinatorics
SimpleGraph.ncard_oddComponents_mono
∀ {V : Type u} (G : SimpleGraph V) [Finite V] {G' : SimpleGraph V},
G ≤ G' → G'.oddComponents.ncard ≤ G.oddComponents.ncard- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- SimpleGraphstatement and proof · cited by 3,072
- Finitestatement and proof · cited by 3,029
- Set.Nonemptyproof · cited by 2,627
- Oddproof · cited by 364
- Set.ncardstatement and proof · cited by 344
- Subtype.val_injectiveproof · cited by 232
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- Set.Nonempty.someproof · cited by 53
- Set.Nonempty.some_memproof · cited by 42
- SimpleGraph.ConnectedComponent.suppproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTutteViolator.monoproof · cited by 1