Generalized skeletal expansion conjecture for colored regular graphs

Let $\Gamma$ be a regular $(n+1)$-valent graph with a “good” $(\mathbb Z_2)^{n+1}$-coloring $\alpha$. A generalized $(n+1)$-skeletal expansion is an expansion denoted $(M,\mathfrak E)$, where $M$ is the resulting space and $\mathfrak E$ records the generalized expansion data. Generalized skeletal expansion conjecture. The pair $(\Gamma,\alpha)$ always admits a generalized $(n+1)$-skeletal expansion $(M,\mathfrak E)$ such that $M$ is a compact $(n+1)$-manifold with boundary. Examples show that generalized expansions can exist even when ordinary skeletal expansions do not; the proposed conjecture asserts existence in every case, and no resolution is supplied here.