Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsCycle.isPath_tail
∀ {V : Type u} {G : SimpleGraph V} {u : V} {p : G.Walk u u}, p.IsCycle → p.tail.IsPath- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.IsPathstatement · cited by 140
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.Walk.sndstatement · cited by 56
- SimpleGraph.Walk.tailstatement · cited by 34
- SimpleGraph.Walk.IsCycle.not_nilproof · cited by 14
- SimpleGraph.Walk.support_tail_of_not_nilproof · cited by 11
- SimpleGraph.Walk.IsCycle.support_nodupproof · cited by 8
- SimpleGraph.Walk.IsPath.mk'proof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.isAcyclic_iff_subsingleton_pathproof · cited by 3
- SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_lengthproof · cited by 1
- SimpleGraph.Walk.IsCycle.isPath_dropproof · cited by 0
- SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_length_eqproof · cited by 0