Theorems · Theorem · combinatorics
SimpleGraph.Colorable.chromaticNumber_pos
∀ {V : Type u} {G : SimpleGraph V} [Nonempty V] {n : ℕ}, G.Colorable n → 0 < G.chromaticNumber- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- lt_of_lt_of_leproof · cited by 438
- Nonempty.someproof · cited by 340
- Classical.arbitraryproof · cited by 161
- Nat.cast_posproof · cited by 113
- SimpleGraph.Colorablestatement and proof · cited by 67
- SimpleGraph.chromaticNumberstatement · cited by 54
- le_csInfproof · cited by 36
- SimpleGraph.Colorable.chromaticNumber_eq_sInfproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.chromaticNumber_botproof · cited by 0
- SimpleGraph.chromaticNumber_posproof · cited by 0