Theorems · Theorem · combinatorics
SimpleGraph.Coloring.valid
∀ {V : Type u} {G : SimpleGraph V} {α : Type u_2} (C : G.Coloring α) {v w : V}, G.Adj v w → C v ≠ C w- Cited by
- 11 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.completeGraphstatement · cited by 49
- SimpleGraph.Coloringstatement and proof · cited by 44
- RelHom.map_relproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- SimpleGraph.two_le_chromaticNumber_of_adjproof · cited by 3
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2
- SimpleGraph.colorable_iff_forall_connectedComponentproof · cited by 2
- SimpleGraph.Coloring.not_adj_of_mem_colorClassproof · cited by 1
- SimpleGraph.IsFiveWheelLike.not_colorable_succproof · cited by 1
- SimpleGraph.Coloring.even_length_iff_congrproof · cited by 1
- SimpleGraph.Coloring.injective_comp_of_pairwise_adjproof · cited by 1
- SimpleGraph.Colorable.mapproof · cited by 0
- SimpleGraph.CompleteBipartiteGraph.chromaticNumberproof · cited by 0
- SimpleGraph.isContained_completeEquipartiteGraph_of_colorableproof · cited by 0
- SimpleGraph.colorable_iff_exists_bdd_nat_coloringproof · cited by 0