Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsCycle.adj_toSubgraph_iff_of_isCycles
∀ {V : Type u_1} {G : SimpleGraph V} {v : V} [G.LocallyFinite] {u : V} {p : G.Walk u u},
p.IsCycle → G.IsCycles → v ∈ p.toSubgraph.verts → ∀ (w : V), p.toSubgraph.Adj v w ↔ G.Adj v w- Cited by
- 0 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SimpleGraph.LocallyFinite
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- Setstatement · cited by 53,352
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Cardinalproof · cited by 2,598
- SimpleGraph.Adjstatement · cited by 1,346
- Cardinal.mkproof · cited by 942
- SimpleGraph.Walkstatement and proof · cited by 915
- Set.ncardproof · cited by 344
- Nonempty.someproof · cited by 340
- SimpleGraph.neighborSetproof · cited by 257
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- Set.toFiniteproof · cited by 174
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