Theorems · Theorem · combinatorics
SimpleGraph.not_cliqueFree_of_isTuranMaximal
∀ {V : Type u_1} [inst : Fintype V] {G : SimpleGraph V} [inst_1 : DecidableRel G.Adj] {r : ℕ},
r ≤ Fintype.card V → G.IsTuranMaximal r → ¬G.CliqueFree rAn r + 1-cliquefree Turán-maximal graph is _not_ r-cliquefree
if it can accommodate such a clique.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- LE.le.trans_eqproof · cited by 328
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- SimpleGraph.CliqueFreestatement and proof · cited by 70
- SimpleGraph.IsTuranMaximalstatement and proof · cited by 19
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