Theorems · Theorem · combinatorics
SimpleGraph.Connected.preconnected
∀ {V : Type u} {G : SimpleGraph V}, G.Connected → G.Preconnected- Cited by
- 28 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Connectedstatement and proof · cited by 75
- SimpleGraph.Preconnectedstatement · cited by 49
Cited by28
Results whose statement or proof uses this declaration.
- SimpleGraph.Connected.exists_isPathproof · cited by 4
- SimpleGraph.Connected.monoproof · cited by 3
- SimpleGraph.Connected.exists_walk_length_eq_distproof · cited by 2
- SimpleGraph.isTree_iff_existsUnique_pathproof · cited by 1
- SimpleGraph.Connected.boxProdproof · cited by 1
- SimpleGraph.connected_iff_ediam_ne_topproof · cited by 1
- SimpleGraph.ConnectedComponent.maximal_connected_induce_suppproof · cited by 1
- SimpleGraph.ConnectedComponent.maximal_connected_toSubgraphproof · cited by 1
- SimpleGraph.Connected.dist_eq_zero_iffproof · cited by 1
- SimpleGraph.Connected.mapproof · cited by 1
- SimpleGraph.Connected.maximal_le_isAcyclic_iff_isTreeproof · cited by 1
- SimpleGraph.exists_isTutteViolatorproof · cited by 1