Theorems · Theorem · combinatorics
SimpleGraph.egirth_le_length
∀ {α : Type u_1} {G : SimpleGraph α} {a : α} {w : G.Walk a a}, w.IsCycle → G.egirth ≤ ↑w.length- Defined in
- Mathlib.Combinatorics.SimpleGraph.Girth
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- le_rflproof · cited by 1,558
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.lengthstatement · cited by 212
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.egirthstatement · cited by 17
- SimpleGraph.le_egirthproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.IsContained.egirth_leproof · cited by 2
- SimpleGraph.Walk.IsCircuit.egirth_le_lengthproof · cited by 1
- SimpleGraph.egirth_topproof · cited by 1
- SimpleGraph.girth_le_lengthproof · cited by 0