Angle Covers: Algorithms and Complexity
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 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.
Cite
@article{arxiv.1911.02040,
title = {Angle Covers: Algorithms and Complexity},
author = {William Evans and Ellen Gethner and Jack Spalding-Jamieson and Alexander Wolff},
journal= {arXiv preprint arXiv:1911.02040},
year = {2022}
}