Theorems · Theorem · combinatorics

SimpleGraph.IsFiveWheelLike.not_colorable_succ

∀ {α : Type u_1} {s : Finset α} {G : SimpleGraph α} {r k : ℕ} [inst : DecidableEq α] {v w₁ w₂ : α} {t : Finset α},
  G.IsFiveWheelLike r k v w₁ w₂ s t → ¬G.Colorable (r + 1)

Any graph containing an IsFiveWheelLike r k structure is not (r + 1)-colorable.

Defined in: Mathlib.Combinatorics.SimpleGraph.FiveWheelLike
Cited by: 1 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites24

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Finsetstatement and proof · cited by 13,712
SetLike.coeproof · cited by 8,199
Set.univproof · cited by 3,945
SimpleGraphstatement and proof · cited by 3,072
Fintype.card_finproof · cited by 270
Set.SurjOnproof · cited by 186
Finset.coe_insertproof · cited by 124
SimpleGraph.Colorablestatement and proof · cited by 67
SimpleGraph.Coloringproof · cited by 44
SimpleGraph.IsFiveWheelLikestatement and proof · cited by 25

Cited by1

Results whose statement or proof uses this declaration.

SimpleGraph.colorable_iff_isCompleteMultipartite_of_maximal_cliqueFreeproof · cited by 0