Theorems · Theorem · combinatorics
SimpleGraph.edgeSet_replaceVertex_of_not_adj
∀ {V : Type u_1} (G : SimpleGraph V) {s t : V} [inst : DecidableEq V],
¬G.Adj s t → (G.replaceVertex s t).edgeSet = G.edgeSet \ G.incidenceSet t ∪ (fun x => s(x, t)) '' G.neighborSet s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.imagestatement and proof · cited by 5,609
- SimpleGraphstatement and proof · cited by 3,072
- Set.extproof · cited by 2,266
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Sym2statement and proof · cited by 737
- Sym2.mkstatement and proof · cited by 332
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.incidenceSetstatement and proof · cited by 46
- SimpleGraph.replaceVertexstatement · cited by 15
- SimpleGraph.adj_commproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.edgeFinset_replaceVertex_of_not_adjproof · cited by 1