Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsHamiltonian.length_eq
∀ {α : Type u_1} [inst : DecidableEq α] {G : SimpleGraph α} {a b : α} {p : G.Walk a b} [inst_1 : Fintype α],
p.IsHamiltonian → p.length = Fintype.card α - 1The length of a Hamiltonian path is one less than the number of vertices of the graph.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- Fintype.cardstatement and proof · cited by 1,386
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.supportproof · cited by 307
- SimpleGraph.Walk.lengthstatement · cited by 212
- List.toFinsetproof · cited by 108
- Finset.card_univproof · cited by 58
- SimpleGraph.Walk.IsHamiltonianstatement and proof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsHamiltonianCycle.length_eqproof · cited by 1
- SimpleGraph.Walk.isHamiltonian_iff_isPath_and_length_eqproof · cited by 1