Theorems · Theorem · combinatorics
SimpleGraph.Connected.nonempty
∀ {V : Type u} {G : SimpleGraph V}, G.Connected → Nonempty V- Cited by
- 9 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
Cited by9
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTree.card_edgeFinsetproof · cited by 3
- SimpleGraph.Connected.maximal_le_isAcyclic_iff_isTreeproof · cited by 1
- SimpleGraph.Connected.ofBoxProdLeftproof · cited by 1
- SimpleGraph.Connected.ofBoxProdRightproof · cited by 1
- SimpleGraph.isTree_iff_existsUnique_pathproof · cited by 1
- SimpleGraph.Connected.boxProdproof · cited by 1
- SimpleGraph.isTree_iff_maximal_isAcyclicproof · cited by 0
- SimpleGraph.ConnectedComponent.maximal_connected_induce_iffproof · cited by 0
- SimpleGraph.induce_sUnion_connected_of_pairwise_not_disjointproof · cited by 0