  Let $\Gamma$ be a finite graph and let $\Gamma^{\mathrm{e}}$ be its extension
graph. We inductively define a sequence $\{\Gamma_i\}$ of finite induced
subgraphs of $\Gamma^{\mathrm{e}}$ through successive applications of an
operation called "doubling along a star". Then we show that every finite
induced subgraph of $\Gamma^{\mathrm{e}}$ is isomorphic to an induced subgraph
of some $\Gamma_i$.
