Theorems · Theorem · combinatorics
SimpleGraph.isTree_of_minimal_connected
∀ {V : Type u_1} {G : SimpleGraph V}, Minimal SimpleGraph.Connected G → G.IsTreeA minimally connected graph is a tree.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- SimpleGraph.Adjproof · cited by 1,346
- Sym2.mkproof · cited by 332
- SimpleGraph.edgeSetproof · cited by 199
- Minimalstatement and proof · cited by 150
- SimpleGraph.Connectedstatement and proof · cited by 75
- by_contraproof · cited by 60
- SimpleGraph.fromEdgeSetproof · cited by 43
- SimpleGraph.IsTreestatement · cited by 32
- SimpleGraph.IsBridgeproof · cited by 30
- Minimal.propproof · cited by 23
- SimpleGraph.edgeSet_fromEdgeSetproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.isTree_iff_minimal_connectedproof · cited by 0