Special Issue on Selected Papers from the 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
Angle Covers: Algorithms and Complexity
William Evans, Ellen Gethner, Jack Spalding-Jamieson, and Alexander Wolff
Vol. 25, no. 2, pp. 643-661, 2021. Regular paper.
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 without a degree-3 vertex 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.

 This work is licensed under the terms of the CC-BY license.
Submitted: June 2020.
Reviewed: November 2020.
Revised: January 2021.
Reviewed: February 2021.
Revised: March 2021.
Accepted: September 2021.
Final: October 2021.
Published: November 2021.
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