Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsCycle.count_support
∀ {V : Type u} {G : SimpleGraph V} {v : V} [inst : DecidableEq V] {c : G.Walk v v},
c.IsCycle → List.count v c.support = 2- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
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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.supportstatement and proof · cited by 307
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.Walk.IsCycle.not_nilproof · cited by 14
- List.count_eq_one_of_memproof · cited by 12
- SimpleGraph.Walk.IsCycle.support_nodupproof · cited by 8
- SimpleGraph.Walk.support_ne_nilproof · cited by 5
- SimpleGraph.Walk.head_supportproof · cited by 4
- SimpleGraph.Walk.end_mem_tail_supportproof · cited by 2
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