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arXiv · 2507.21864

Pathwidth of 2-Layer $k$-Planar Graphs

Yuto Okada
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Abstract

A bipartite graph $G = (X \cup Y, E)$ is a 2-layer $k$-planar graph if it admits a drawing on the plane such that the vertices in $X$ and $Y$ are placed on two parallel lines respectively, edges are drawn as straight-line segments, and every edge involves at most $k$ crossings. Angelini, Da Lozzo, F\"orster, and Schneck [GD 2020; Comput. J., 2024] showed that every 2-layer $k$-planar graph has pathwidth at most $k + 1$. In this paper, we show that this bound is sharp by giving a 2-layer $k$-planar graph with pathwidth $k + 1$ for every $k \geq 0$. This improves their lower bound of $(k+3)/2$.

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Yuto Okada. 2025-07-29. Pathwidth of 2-Layer $k$-Planar Graphs. https://doi.org/10.57717/cgt.v5i1.101

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