Theorems · Theorem · combinatorics
SimpleGraph.degree_eq_card_sub_one
∀ {V : Type u_1} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj] (v : V),
G.degree v = Fintype.card V - 1 ↔ G.IsUniversal v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.degreestatement and proof · cited by 112
- SimpleGraph.neighborFinsetproof · cited by 72
- Finset.card_insert_of_notMemproof · cited by 45
- Finset.card_erase_of_memproof · cited by 38
- Fintype.card_pos_iffproof · cited by 31
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