On the asphericity of a family of positive relative group presentations - Aldwaik, Suzana; Edjvet, Martin (Cambridge University Press, 2017)
Excluding four exceptional cases, the asphericity of the relative presentation P= ⟨G; x|xmgxh⟩ for m ≥ 2 is determined. If H = ⟨g; h⟩ ≤ G, then the exceptional cases occur when H is isomorphic to C5 or C6.