Theorems · Theorem · combinatorics
SimpleGraph.Coloring.colorable
∀ {V : Type u} {G : SimpleGraph V} {α : Type u_2} [inst : Fintype α] (C : G.Coloring α), G.Colorable (Fintype.card α)- Cited by
- 12 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Fintype.cardstatement and proof · cited by 1,386
- Fintype.card_finproof · cited by 270
- SimpleGraph.Colorablestatement · cited by 67
- SimpleGraph.Coloringstatement and proof · cited by 44
- SimpleGraph.recolorOfCardLEproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- SimpleGraph.chromaticNumber_topproof · cited by 4
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2
- SimpleGraph.colorable_of_fintypeproof · cited by 1
- SimpleGraph.eq_top_of_chromaticNumber_eq_cardproof · cited by 1
- SimpleGraph.Partition.colorableproof · cited by 1
- SimpleGraph.completeMultipartiteGraph.colorableproof · cited by 1
- SimpleGraph.completeMultipartiteGraph.colorable_of_cliqueFreeproof · cited by 1
- SimpleGraph.chromaticNumber_pathGraphproof · cited by 0
- SimpleGraph.chromaticNumber_cycleGraph_of_evenproof · cited by 0
- SimpleGraph.chromaticNumber_cycleGraph_of_oddproof · cited by 0
- SimpleGraph.IsClique.card_le_of_coloringproof · cited by 0
- SimpleGraph.CompleteBipartiteGraph.chromaticNumberproof · cited by 0