Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.isSpanning_iff
∀ {V : Type u} {G : SimpleGraph V} {G' : G.Subgraph}, G'.IsSpanning ↔ G'.verts = Set.univ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement · cited by 3,945
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.Subgraph.vertsstatement · cited by 210
- Set.eq_univ_iff_forallproof · cited by 93
- SimpleGraph.Subgraph.IsSpanningstatement · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.IsSpanning.card_vertsproof · cited by 1
- SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_suppproof · cited by 1
- SimpleGraph.Subgraph.IsSpanning.verts_eq_univproof · cited by 1
- SimpleGraph.exists_isPerfectMatching_of_forall_ncard_leproof · cited by 0