Theorems · Theorem · combinatorics
SimpleGraph.chromaticNumber_le_iff_colorable
∀ {V : Type u} {G : SimpleGraph V} {n : ℕ}, G.chromaticNumber ≤ ↑n ↔ G.Colorable n- Cited by
- 10 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- InfSet.sInfproof · cited by 935
- LT.lt.neproof · cited by 872
- Nat.cast_leproof · cited by 159
- Set.mem_ofPred_eqproof · cited by 122
- SimpleGraph.Colorablestatement and proof · cited by 67
- SimpleGraph.chromaticNumberstatement and proof · cited by 54
- Nat.sInf_memproof · cited by 15
- SimpleGraph.Colorable.chromaticNumber_leproof · cited by 11
Cited by10
Results whose statement or proof uses this declaration.
- SimpleGraph.chromaticNumber_le_of_forall_impproof · cited by 4
- SimpleGraph.two_le_chromaticNumber_of_adjproof · cited by 3
- SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loopproof · cited by 2
- SimpleGraph.eq_top_of_chromaticNumber_eq_cardproof · cited by 1
- SimpleGraph.chromaticNumber_eq_one_iffproof · cited by 1
- SimpleGraph.chromaticNumber_eq_zero_iffproof · cited by 1
- SimpleGraph.chromaticNumber_le_two_iff_isBipartiteproof · cited by 1
- SimpleGraph.chromaticNumber_sumproof · cited by 0
- SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorableproof · cited by 0
- SimpleGraph.chromaticNumber_le_one_of_subsingletonproof · cited by 0