Theorems · Theorem · combinatorics
SimpleGraph.egirth_eq_top
∀ {α : Type u_1} {G : SimpleGraph α}, G.egirth = ⊤ ↔ G.IsAcyclic- Defined in
- Mathlib.Combinatorics.SimpleGraph.Girth
- Cited by
- 4 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- ENatstatement · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkproof · cited by 915
- SimpleGraph.Walk.lengthproof · cited by 212
- SimpleGraph.Walk.IsCycleproof · cited by 91
- SimpleGraph.IsAcyclicstatement · cited by 67
- SimpleGraph.egirthstatement · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.three_le_girthproof · cited by 1
- SimpleGraph.IsAcyclic.egirth_eq_topproof · cited by 1
- SimpleGraph.IsContained.girth_leproof · cited by 0
- SimpleGraph.girth_antiproof · cited by 0