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Theorems · Definition · combinatorics

SimpleGraph.Subgraph.neighborSet

{V : Type u} → {G : SimpleGraph V} → G.Subgraph → V → Set V

G'.neighborSet v is the set of vertices adjacent to v in G'.

Defined in
Mathlib.Combinatorics.SimpleGraph.Subgraph
Cited by
46 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms

Around this declaration

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

SimpleGraph.Subgraph.degree · cited by 14Subgraph.degreeSimpleGraph.Subgraph.neighborSet_subset · cited by 4Subgraph.neighborSet_subs…SimpleGraph.Walk.IsCycle.ncard_neighborSet_toSubgraph_eq_two · cited by 3IsCycle.ncard_neighborSet…SimpleGraph.Subgraph.adj_iff_of_neighborSet_equiv · cited by 3Subgraph.adj_iff_of_neigh…SimpleGraph.Subgraph.coe_degree · cited by 3Subgraph.coe_degreeSimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_endpoint · cited by 2IsCycle.neighborSet_toSub…SimpleGraph.Subgraph.degree_eq_zero_of_subsingleton · cited by 2Subgraph.degree_eq_zero_o…SimpleGraph.neighborSet_fst_subgraphOfAdj · cited by 2SimpleGraph.neighborSet_f…SimpleGraph.Walk.finite_neighborSet_toSubgraph · cited by 1Walk.finite_neighborSet_t…SimpleGraph.Walk.IsCycle.neighborSet_toSubgraph_internal · cited by 1IsCycle.neighborSet_toSub…SimpleGraph.Subgraph.coeNeighborSetEquiv · cited by 1Subgraph.coeNeighborSetEq…SimpleGraph.Subgraph.degree_of_notMem_verts · cited by 1Subgraph.degree_of_notMem…SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internal · cited by 1IsPath.neighborSet_toSubg…SimpleGraph.Subgraph.finset_card_neighborSet_eq_degree · cited by 1Subgraph.finset_card_neig…SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_startpoint · cited by 1IsPath.neighborSet_toSubg…Set · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Subgraph · cited by 326SimpleGraph.SubgraphSimpleGraph.Subgraph.Adj · cited by 147Subgraph.AdjSubgraph.neighborSetCITED BYCITES

Cites5

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

Cited by49

Results whose statement or proof uses this declaration.