Theorems · Theorem · combinatorics
SimpleGraph.vertexCoverNum_exists
∀ {V : Type u_1} (G : SimpleGraph V), ∃ s, s.encard = G.vertexCoverNum ∧ G.IsVertexCover s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 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.
- Setstatement and proof · cited by 53,352
- ENatstatement · cited by 4,985
- Set.univproof · cited by 3,945
- SimpleGraphstatement and proof · cited by 3,072
- iInfproof · cited by 1,690
- Set.encardstatement and proof · cited by 327
- nonempty_subtypeproof · cited by 22
- SimpleGraph.IsVertexCoverstatement and proof · cited by 17
- SimpleGraph.vertexCoverNumstatement · cited by 17
- iInf_subtypeproof · cited by 12
- ENat.exists_eq_iInfproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNumproof · cited by 3
- SimpleGraph.exists_of_le_vertexCoverNumproof · cited by 1
- SimpleGraph.vertexCoverNum_eq_zeroproof · cited by 0