### Abstract

The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove that, up to a finite number of well specified exceptions of constant size, the number of edges of a graph with n vertices and a total angular resolution greater than 60 is bounded by 2n-6. This bound is tight. In addition, we show that deciding whether a graph has total angular resolution at least 60 is NP-hard.

Original language | English |
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Title of host publication | Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings |

Editors | Daniel Archambault, Csaba D. Tóth |

Publisher | Springer |

Pages | 193-199 |

Number of pages | 7 |

ISBN (Print) | 9783030358013 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

Externally published | Yes |

Event | 27th International Symposium on Graph Drawing and Network Visualization, GD 2019 - Prague, Czech Republic Duration: 2019 Sep 17 → 2019 Sep 20 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11904 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 27th International Symposium on Graph Drawing and Network Visualization, GD 2019 |
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Country | Czech Republic |

City | Prague |

Period | 19/9/17 → 19/9/20 |

### Keywords

- Angular resolution
- Crossing resolution
- Graph drawing
- NP-hardness
- Total angular resolution

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings*(pp. 193-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11904 LNCS). Springer. https://doi.org/10.1007/978-3-030-35802-0_15