Theorems · Theorem · combinatorics
SimpleGraph.exists_maximal_isAcyclic_of_le_isAcyclic
∀ {V : Type u_1} {G H : SimpleGraph V}, H ≤ G → H.IsAcyclic → ∃ H', H ≤ H' ∧ Maximal (fun H => H ≤ G ∧ H.IsAcyclic) H'Every acyclic subgraph H ≤ G is contained in a maximal such subgraph.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- SimpleGraphstatement and proof · cited by 3,072
- SupSet.sSupproof · cited by 954
- Maximalstatement · cited by 211
- IsChainproof · cited by 158
- le_sSupproof · cited by 79
- SimpleGraph.IsAcyclicstatement and proof · cited by 67
- IsChain.directedOnproof · cited by 28
- zorn_le_nonempty₀proof · cited by 13
- SimpleGraph.isAcyclic_sSup_of_isAcyclic_directedOnproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.exists_isAcyclic_reachable_eq_le_of_le_of_isAcyclicproof · cited by 3