Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsEulerian.even_degree_iff
∀ {V : Type u_1} {G : SimpleGraph V} [inst : DecidableEq V] {x u v : V} {p : G.Walk u v},
p.IsEulerian → ∀ [inst : Fintype V] [inst_1 : DecidableRel G.Adj], Even (G.degree x) ↔ u ≠ v → x ≠ u ∧ x ≠ v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Trails
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Multisetproof · cited by 2,627
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterproof · cited by 949
- SimpleGraph.Walkstatement and proof · cited by 915
- Sym2proof · cited by 737
- Evenstatement and proof · cited by 444
- Finset.valproof · cited by 438
- Multiset.cardproof · cited by 375
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsEulerian.card_filter_odd_degreeproof · cited by 1