Theorems · Theorem · combinatorics
SimpleGraph.Colorable.card_le_of_pairwise_adj
∀ {V : Type u} {G : SimpleGraph V} {n : ℕ} {ι : Type u_1},
G.Colorable n → ∀ (f : ι → V), (Pairwise fun i j => G.Adj (f i) (f j)) → Nat.card ι ≤ n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Nat.cardstatement and proof · cited by 844
- Pairwisestatement and proof · cited by 516
- Fintype.card_finproof · cited by 270
- Nat.card_eq_fintype_cardproof · cited by 200
- SimpleGraph.Colorablestatement and proof · cited by 67
- SimpleGraph.Coloringproof · cited by 44
- Nat.card_le_card_of_injectiveproof · cited by 19
- SimpleGraph.Coloring.injective_comp_of_pairwise_adjproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.IsClique.card_le_of_colorableproof · cited by 2
- SimpleGraph.le_chromaticNumber_of_pairwise_adjproof · cited by 1