Abstract

Let S<inf>g</inf><inf>,</inf><inf>n</inf> be an orientable surface of genus g with n punctures. We identify a finite rigid subgraph X<inf>g</inf><inf>,</inf><inf>n</inf> of the pants graph P(S<inf>g</inf><inf>,</inf><inf>n</inf>) , that is, a subgraph with the property that any simplicial embedding of X<inf>g</inf><inf>,</inf><inf>n</inf> into any pants graph P(Sg′,n′) is induced by an embedding Sg,n→Sg′,n′. This extends results of the third author for the case of genus zero surfaces.