Theorems · Theorem · combinatorics

SimpleGraph.IsFiveWheelLike.isPathGraph3Compl

∀ {α : Type u_1} [inst : DecidableEq α] {G : SimpleGraph α} {r k : ℕ} {v w₁ w₂ : α} {s t : Finset α},
  G.IsFiveWheelLike r k v w₁ w₂ s t → G.IsPathGraph3Compl v w₁ w₂

{v, w₁, w₂} induces the single edge w₁w₂

Defined in: Mathlib.Combinatorics.SimpleGraph.FiveWheelLike
Cited by: 4 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: DecidableEq

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Cites4

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

Finsetstatement and proof · cited by 13,712
SimpleGraphstatement and proof · cited by 3,072
SimpleGraph.IsFiveWheelLikestatement and proof · cited by 25
SimpleGraph.IsPathGraph3Complstatement · cited by 12

Cited by4

Results whose statement or proof uses this declaration.

SimpleGraph.IsFiveWheelLike.card_inter_lt_of_cliqueFreeproof · cited by 2
SimpleGraph.IsFiveWheelLike.fst_notMem_rightproof · cited by 1
SimpleGraph.IsFiveWheelLike.not_colorable_succproof · cited by 1
SimpleGraph.IsFiveWheelLike.minDegree_le_of_cliqueFree_fiveWheelLikeFree_succproof · cited by 1