Theorems · Theorem · combinatorics
SimpleGraph.IsBipartiteWith.mem_of_mem_adj
∀ {V : Type u_1} {v w : V} {G : SimpleGraph V} {s t : Set V}, G.IsBipartiteWith s t → v ∈ s → G.Adj v w → w ∈ tIf G.IsBipartiteWith s t and v ∈ s, then if v is adjacent to w in G then w ∈ t.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Set.disjoint_leftproof · cited by 121
- SimpleGraph.IsBipartiteWithstatement and proof · cited by 42
- SimpleGraph.IsBipartiteWith.disjointproof · cited by 11
- SimpleGraph.IsBipartiteWith.mem_of_adjproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.isBipartiteWith_neighborFinsetproof · cited by 2
- SimpleGraph.isBipartiteWith_neighborSetproof · cited by 1