Theorems · Theorem · combinatorics
SimpleGraph.IsTree.connected
∀ {V : Type u_1} {G : SimpleGraph V}, G.IsTree → G.Connected- 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.
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 · cited by 75
- SimpleGraph.IsTreestatement and proof · cited by 32
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.IsTree.dist_ne_of_adjproof · cited by 0
- SimpleGraph.IsTree.exists_ne_and_degree_eq_oneproof · cited by 0
- SimpleGraph.IsTree.isConnectedproof · cited by 0
- SimpleGraph.IsTree.minDegree_eq_one_of_nontrivialproof · cited by 0
- SimpleGraph.isTree_iff_connected_and_cardproof · cited by 0
- SimpleGraph.isTree_iff_maximal_isAcyclicproof · cited by 0
- SimpleGraph.isTree_iff_minimal_connectedproof · cited by 0