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arXiv · 1911.02040

Angle Covers: Algorithms and Complexity

William Evans·Ellen Gethner·Jack Spalding-Jamieson·Alexander Wolff
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Abstract

Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each edge participates in at least one such pair. We show that any graph of maximum degree 4 admits an angle cover, give a poly-time algorithm for deciding if a graph with no degree-3 vertices has an angle-cover, and prove that, given a graph of maximum degree 5, it is NP-hard to decide whether it admits an angle cover. We also consider extensions of the angle cover problem where every vertex selects a fixed number $a>1$ of angles or where an angle consists of more than two consecutive edges. We show an application of angle covers to the problem of deciding if the 2-blowup of a planar graph has isomorphic thickness 2.

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William Evans, Ellen Gethner, Jack Spalding-Jamieson, Alexander Wolff. 2019-11-05. Angle Covers: Algorithms and Complexity. https://doi.org/10.7155/jgaa.00576

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