Theorems · Theorem · combinatorics
SimpleGraph.Reachable.one_lt_dist_of_ne_of_not_adj
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, G.Reachable u v → u ≠ v → ¬G.Adj u v → 1 < G.dist u v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 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.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.Walkproof · cited by 915
- SimpleGraph.Walk.lengthproof · cited by 212
- SimpleGraph.Reachablestatement and proof · cited by 141
- SimpleGraph.diststatement and proof · cited by 40
- SimpleGraph.Reachable.exists_walk_length_eq_distproof · cited by 5
- SimpleGraph.Reachable.pos_dist_of_neproof · cited by 1
- SimpleGraph.Walk.exists_length_eq_one_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.exists_isTutteViolatorproof · cited by 1
- SimpleGraph.Connected.one_lt_dist_of_ne_of_not_adjproof · cited by 0