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feat(Combinators/SimpleGraph/Hamiltonian): p.support.length = Fintype.card α #30206

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feat(Combinators/SimpleGraph/Hamiltonian): p.support.length = Fintype.card α #30206

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feat(Combinators/SimpleGraph/Hamiltonian): `p.support.length = Fintyp…
SnirBroshi Oct 11, 2025
4aee8ca
chore(Combinatorics/SimpleGraph/Hamiltonian): golf `support_length_eq`
SnirBroshi Oct 11, 2025
970be23
chore(Combinatorics/SimpleGraph/Hamiltonian): rename `support_length_…
SnirBroshi Oct 18, 2025
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5 changes: 5 additions & 0 deletions Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean
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Expand Up @@ -69,6 +69,11 @@ lemma IsHamiltonian.length_eq (hp : p.IsHamiltonian) : p.length = Fintype.card
rw [← length_support, ← List.sum_toFinset_count_eq_length, Finset.sum_congr rfl fun _ _ ↦ hp _,
← card_eq_sum_ones, hp.support_toFinset, card_univ]

/-- The length of the support of a Hamiltonian path equals the number of vertices of the graph. -/
lemma IsHamiltonian.length_support (hp : p.IsHamiltonian) : p.support.length = Fintype.card α := by
have : Inhabited α := ⟨a⟩
grind [Fintype.card_ne_zero, length_support, length_eq]

end

/-- A Hamiltonian cycle is a cycle that visits every vertex once. -/
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