Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsCycle.not_nil
∀ {V : Type u} {G : SimpleGraph V} {v : V} {p : G.Walk v v}, p.IsCycle → ¬p.Nil- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
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
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.Nilstatement and proof · cited by 102
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.Walk.IsCycle.isCircuitproof · cited by 14
- SimpleGraph.Walk.IsCircuit.ne_nilproof · cited by 6
- SimpleGraph.Walk.Nil.eq_nilproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsCycle.getVert_injOnproof · cited by 4
- SimpleGraph.Walk.IsCycle.isPath_tailproof · cited by 4
- SimpleGraph.isAcyclic_iff_forall_isBridgeproof · cited by 4
- SimpleGraph.isAcyclic_iff_subsingleton_pathproof · cited by 3
- SimpleGraph.Walk.IsHamiltonianCycle.mem_supportproof · cited by 2
- SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpointproof · cited by 2
- SimpleGraph.Walk.IsHamiltonianCycle.length_eqproof · cited by 1
- SimpleGraph.Walk.IsCycle.isPath_dropLastproof · cited by 1
- SimpleGraph.cycleGraph_isContained_iffproof · cited by 1
- SimpleGraph.Walk.IsHamiltonianCycle.count_support_selfproof · cited by 0
- SimpleGraph.IsTree.coe_subgraphOfAdjproof · cited by 0
- SimpleGraph.not_isHamiltonian_bot_of_card_ne_oneproof · cited by 0