# Angle Covers: Algorithms and Complexity

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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research
12/27/2018

### Above guarantee parameterization for vertex cover on graphs with maximum degree 4

In the vertex cover problem, the input is a graph G and an integer k, an...
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### Computational Complexity of Flattening Fixed-Angle Orthogonal Chains

Planar/flat configurations of fixed-angle chains and trees are well stud...
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### The graph tessellation cover number: extremal bounds, efficient algorithms and hardness

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### Vertex Covers Revisited: Indirect Certificates and FPT Algorithms

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### Partial vertex covers and the complexity of some problems concerning static and dynamic monopolies

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### Minimum Scan Cover and Variants – Theory and Experiments

We consider a spectrum of geometric optimization problems motivated by c...
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### Angle-Based Sensor Network Localization

This paper studies angle-based sensor network localization (ASNL) in a p...