Theorems · Theorem · combinatorics
SimpleGraph.isTree_iff_connected_and_card
∀ {V : Type u_1} {G : SimpleGraph V} [Finite V], G.IsTree ↔ G.Connected ∧ Nat.card ↑G.edgeSet + 1 = Nat.card V- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finitestatement and proof · cited by 3,029
- Finset.cardproof · cited by 2,327
- Fintype.cardproof · cited by 1,386
- SimpleGraph.Adjproof · cited by 1,346
- Finset.filterproof · cited by 949
- Nat.cardstatement and proof · cited by 844
- Sym2statement · cited by 737
- Sym2.mkproof · cited by 332
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