Let Γ be a connected G-vertex-transitive graph, let v be a vertex of Γ and let GΓ(v) v be the permutation group induced by the action of the vertex-stabilizer Gv on the neighbourhood Γ(v). The graph Γ is said to be G-locally primitive if GΓ(v) v is primitive. Weiss conjectured in 1978 that there exists a function f : N → N such that, if Γ is a connected …