Theorems · Theorem · combinatorics
SimpleGraph.IsClique.even_iff_exists_isMatching
∀ {V : Type u_1} {G : SimpleGraph V} {u : Set V},
G.IsClique u → u.Finite → (Even u.ncard ↔ ∃ M, M.verts = u ∧ M.IsMatching)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivproof · cited by 8,337
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Cardinalproof · cited by 2,598
- Disjointproof · cited by 2,201
- Set.Finitestatement and proof · cited by 1,814
- Cardinal.mkproof · cited by 942
- Evenstatement and proof · cited by 444
- Set.ncardstatement and proof · cited by 344
- SimpleGraph.Subgraphstatement and proof · cited by 326
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.IsPerfectMatching.exists_of_isClique_suppproof · cited by 1