Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsCircuit.three_le_length
∀ {V : Type u} {G : SimpleGraph V} {v : V} {p : G.Walk v v}, p.IsCircuit → 3 ≤ p.length- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- zero_addproof · cited by 2,366
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Walk.IsCircuitstatement and proof · cited by 21
- SimpleGraph.Walk.IsCircuit.isTrailproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsCycle.getVert_injOn'proof · cited by 2
- SimpleGraph.three_le_egirthproof · cited by 2
- SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_oneproof · cited by 1
- SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_lengthproof · cited by 1
- SimpleGraph.isAcyclic_iff_free_cycleGraphproof · cited by 1
- SimpleGraph.Walk.IsCycle.snd_ne_penultimateproof · cited by 1
- SimpleGraph.IsAcyclic.of_card_le_twoproof · cited by 1