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Lifting maps between graphs to embeddings

Lifting maps between graphs to embeddings

In this paper, we study conditions for the existence of an embedding $\widetilde{f} \colon P \to Q \times \mathbb{R}$ such that $f = \mathrm{pr}_Q \circ \widetilde{f}$, where $f \colon P \to Q$ is a piecewise linear map between polyhedra. Our focus is on non-degenerate maps between graphs, where non-degeneracy means …