Path-Monotonic Upward Drawings of Graphs

In this paper, we introduce a new problem of finding an upward drawing of a given plane graph \(\gamma \) with a set \(\mathcal {P}\) of paths so that each path in the set is drawn as a poly-line that is monotone in the y-coordinate. We present a sufficient condition for an instance \((\gamma ,\mathcal {P})\) to admit such an upward drawing. We also present a linear-time algorithm to construct such a drawing, which is straight-line for a simple graph, or poly-line otherwise. Our results imply that every 1-plane graph admits an upward drawing.