Theorems · Theorem · combinatorics
SimpleGraph.le_egirth
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ∞}, n ≤ G.egirth ↔ ∀ (a : α) (w : G.Walk a a), w.IsCycle → n ≤ ↑w.length- Defined in
- Mathlib.Combinatorics.SimpleGraph.Girth
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.egirthstatement · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.egirth_le_lengthproof · cited by 4