cliqueFree_bot — Mathlib

English

If there is a finite index set ι with card ι large relative to n, the complete multipartite graph on V has not clique-free n.

Русский

Если индексный набор имеет достаточно большой кардинал, то completeMultipartiteGraph имеет не clique-free n.

LaTeX

$$$ \text{not_cliqueFree_of_le_card} : [Fintype ι] (f: \forall i, V i) (hc: n \le card ι) \Rightarrow \neg (\mathrm{completeMultipartiteGraph} V).IsNClique(n). $$$

Lean4

@[simp]
theorem cliqueFree_bot (h : 2 ≤ n) : (⊥ : SimpleGraph α).CliqueFree n :=
  by
  intro t ht
  have := le_trans h (isNClique_bot_iff.1 ht).1
  contradiction

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