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arXiv · 0802.1312

Untangling polygons and graphs

Josef Cibulka
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Abstract

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at least Ω(n^{2/3}) vertices fixed. For any graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.

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Josef Cibulka. 2008-06-25. Untangling polygons and graphs. https://doi.org/10.1007/s00454-009-9150-x

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