Abstract
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.
Research supported by ARC Discovery Project. For omitted proofs, see [12].
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Hong, SH., Nagamochi, H. (2020). Path-Monotonic Upward Drawings of Graphs. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_9
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