Theorems · Definition · combinatorics
SimpleGraph.egirth
{α : Type u_1} → SimpleGraph α → ℕ∞The extended girth of a simple graph is the length of its smallest cycle, or ∞ if the graph is
acyclic.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Girth
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 32 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 · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- iInfproof · cited by 1,690
- SimpleGraph.Walkproof · cited by 915
- SimpleGraph.Walk.lengthproof · cited by 212
- SimpleGraph.Walk.IsCycleproof · cited by 91
Cited by18
Results whose statement or proof uses this declaration.
- SimpleGraph.girthproof · cited by 11
- SimpleGraph.egirth_eq_topstatement · cited by 4
- SimpleGraph.egirth_le_lengthstatement · cited by 4
- SimpleGraph.IsContained.egirth_lestatement and proof · cited by 2
- SimpleGraph.three_le_egirthstatement · cited by 2
- SimpleGraph.exists_egirth_eq_lengthstatement and proof · cited by 2
- SimpleGraph.egirth_antistatement · cited by 1
- SimpleGraph.egirth_botstatement · cited by 1
- SimpleGraph.egirth_topstatement · cited by 1
- SimpleGraph.le_egirthstatement · cited by 1
- SimpleGraph.Walk.IsCircuit.egirth_le_lengthstatement and proof · cited by 1
- SimpleGraph.Iso.egirth_eqstatement · cited by 1