Theorems · Theorem · combinatorics
SimpleGraph.isAcyclic_iff_pairwise_not_isEdgeReachable_two
∀ {V : Type u_1} {G : SimpleGraph V}, G.IsAcyclic ↔ Pairwise fun x1 x2 => ¬G.IsEdgeReachable 2 x1 x2- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- le_rflproof · cited by 1,558
- SimpleGraph.Walkproof · cited by 915
- Sym2proof · cited by 737
- Pairwisestatement and proof · cited by 516
- SimpleGraph.edgeSetproof · cited by 199
- SimpleGraph.Walk.IsCycleproof · cited by 91
- SimpleGraph.IsAcyclicstatement and proof · cited by 67
- Sym2.Relproof · cited by 43
- SimpleGraph.Adj.neproof · cited by 39
- SimpleGraph.IsEdgeReachablestatement and proof · cited by 24
- SimpleGraph.isAcyclic_iff_forall_isBridgeproof · cited by 4
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