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arXiv · 2312.08355

Disconnected cuts in 4-connected planar graphs

Brandon Du Preez
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Abstract

Let $G=(V,E)$ be a connected graph. A subset $S\subset V$ is a cut of $G$ if $G-S$ is disconnected. A near triangulation is a 2-connected plane graph that has at most one face that is not a triangle. In this paper, we explore minimal cuts of 4-connected planar graphs. Our main result is that every minimal cut of a 4-connected planar graph $G$ is connected if and only if $G$ is a near-triangulation. We use this result to sketch a linear-time algorithm for finding a disconnected cut of a 4-connected planar graph.

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Brandon Du Preez. 2023-12-13. Disconnected cuts in 4-connected planar graphs. https://arxiv.org/abs/2312.08355

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