Theorems · Theorem · combinatorics
SimpleGraph.Preconnected.minDegree_pos_of_nontrivial
∀ {V : Type u} [Nontrivial V] [inst : Fintype V] {G : SimpleGraph V} [inst_1 : DecidableRel G.Adj],
G.Preconnected → 0 < G.minDegree- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Nontrivialstatement and proof · cited by 2,416
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.degreeproof · cited by 112
- SimpleGraph.Preconnectedstatement and proof · cited by 49
- SimpleGraph.minDegreestatement and proof · cited by 25
- SimpleGraph.exists_minimal_degree_vertexproof · cited by 3
- SimpleGraph.Preconnected.degree_pos_of_nontrivialproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTree.minDegree_eq_one_of_nontrivialproof · cited by 0