### Abstract

Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓ_{j} = {(x, j) |x ∈ ℝ}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓ_{j} forms a labeling of the vertices. Such a graph G with the labeling φ is called an n-level graph and is said to be n-level planar if it can be drawn with straight-line edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are n-level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are three-fold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 367-379 |

Number of pages | 13 |

Volume | 4372 LNCS |

State | Published - 2007 |

Event | 14th International Symposium on Graph Drawing, GD 2006 - Karlsruhe, Germany Duration: Sep 18 2006 → Sep 19 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 4372 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 14th International Symposium on Graph Drawing, GD 2006 |
---|---|

Country | Germany |

City | Karlsruhe |

Period | 9/18/06 → 9/19/06 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4372 LNCS, pp. 367-379). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4372 LNCS).

**Characterization of unlabeled level planar trees.** / Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Kobourov, Stephen G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 4372 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4372 LNCS, pp. 367-379, 14th International Symposium on Graph Drawing, GD 2006, Karlsruhe, Germany, 9/18/06.

}

TY - GEN

T1 - Characterization of unlabeled level planar trees

AU - Estrella-Balderrama, Alejandro

AU - Fowler, J. Joseph

AU - Kobourov, Stephen G

PY - 2007

Y1 - 2007

N2 - Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j) |x ∈ ℝ}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an n-level graph and is said to be n-level planar if it can be drawn with straight-line edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are n-level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are three-fold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.

AB - Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j) |x ∈ ℝ}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an n-level graph and is said to be n-level planar if it can be drawn with straight-line edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are n-level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are three-fold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.

UR - http://www.scopus.com/inward/record.url?scp=38149033037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149033037&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540709039

VL - 4372 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 367

EP - 379

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -