### Abstract

In this paper we consider the problem of characterizing the directed graphs that admit an upward straight-line embedding into every point set in convex or in general position. In particular, we show that no biconnected directed graph admits an upward straight-line embedding into every point set in convex position, and we provide a characterization of the Hamiltonian directed graphs that admit upward straight-line embeddings into every point set in general or in convex position. We also describe how to construct upward straight-line embeddings of directed paths into convex point sets and we prove that for directed trees such embeddings do not always exist. Further, we investigate the related problem of upward simultaneous embedding without mapping, proving that deciding whether two directed graphs admit an upward simultaneous embedding without mapping is NP-hard.

Original language | English (US) |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers |

Pages | 122-133 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2008 |

Event | 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 - Durham, United Kingdom Duration: Jun 30 2008 → Jul 2 2008 |

### 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 | 5344 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 |
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Country | United Kingdom |

City | Durham |

Period | 6/30/08 → 7/2/08 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers*(pp. 122-133). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5344 LNCS). https://doi.org/10.1007/978-3-540-92248-3_12