Mathlib Map

Theorems · Theorem · combinatorics

SimpleGraph.Adj.reachable

∀ {V : Type u} {G : SimpleGraph V} {u v : V}, G.Adj u v → G.Reachable u v
Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
17 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms

Around this declaration

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

SimpleGraph.Subgraph.subgraphOfAdj_connected · cited by 3Subgraph.subgraphOfAdj_co…SimpleGraph.isBridge_iff_not_isEdgeReachable_two · cited by 2SimpleGraph.isBridge_iff_…SimpleGraph.ConnectedComponent.connectedComponentMk_eq_of_adj · cited by 2ConnectedComponent.connec…SimpleGraph.ComponentCompl.mem_of_adj · cited by 1ComponentCompl.mem_of_adjSimpleGraph.Subgraph.IsMatching.induce_connectedComponent · cited by 1IsMatching.induce_connect…SimpleGraph.Reachable.of_isUniversal · cited by 1Reachable.of_isUniversalSimpleGraph.reachable_or_compl_adj · cited by 1SimpleGraph.reachable_or_…SimpleGraph.reachable_or_reachable_compl · cited by 1SimpleGraph.reachable_or_…SimpleGraph.Reachable.sum_sup_edge · cited by 1Reachable.sum_sup_edgeSimpleGraph.IsAcyclic.dist_ne_of_adj · cited by 1IsAcyclic.dist_ne_of_adjSimpleGraph.maximal_isAcyclic_iff_reachable_eq · cited by 1SimpleGraph.maximal_isAcy…SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable · cited by 1SimpleGraph.lapMatrix_toL…SimpleGraph.preconnected_top · cited by 0SimpleGraph.preconnected_…SimpleGraph.Adj.diff_dist_adj · cited by 0Adj.diff_dist_adjSimpleGraph.componentComplMk_eq_of_adj · cited by 0SimpleGraph.componentComp…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.Reachable · cited by 141SimpleGraph.ReachableSimpleGraph.Adj.toWalk · cited by 22Adj.toWalkSimpleGraph.Walk.reachable · cited by 7Walk.reachableAdj.reachableCITED BYCITES

Cites5

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

Cited by17

Results whose statement or proof uses this declaration.