Mathlib Map

Theorems · Theorem · combinatorics

SimpleGraph.CliqueFree.comap

∀ {α : Type u_1} {β : Type u_2} {G : SimpleGraph α} {n : ℕ} {H : SimpleGraph β},
  H.IsContained G → G.CliqueFree n → H.CliqueFree n

If a graph is cliquefree, any graph that is contained in it is also cliquefree.

Defined in
Mathlib.Combinatorics.SimpleGraph.Clique
Cited by
2 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.isTuranMaximal_of_iso · cited by 3SimpleGraph.isTuranMaxima…SimpleGraph.IsCompleteMultipartite.colorable_of_cliqueFree · cited by 2IsCompleteMultipartite.co…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.CliqueFree · cited by 70SimpleGraph.CliqueFreeSimpleGraph.IsContained · cited by 68SimpleGraph.IsContainedSimpleGraph.IsContained.trans · cited by 9IsContained.transSimpleGraph.not_cliqueFree_iff_top_isContained · cited by 7SimpleGraph.not_cliqueFre…CliqueFree.comapCITED BYCITES

Cites5

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

Cited by2

Results whose statement or proof uses this declaration.