Characterization of unlabeled level planar trees

Alejandro Estrella-Balderrama, J. Joseph Fowler, Stephen G. Kobourov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationGraph Drawing - 14th International Symposium, GD 2006, Revised Papers
Pages367-379
Number of pages13
StatePublished - Dec 1 2007
Event14th International Symposium on Graph Drawing, GD 2006 - Karlsruhe, Germany
Duration: Sep 18 2006Sep 19 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4372 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th International Symposium on Graph Drawing, GD 2006
CountryGermany
CityKarlsruhe
Period9/18/069/19/06

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Estrella-Balderrama, A., Fowler, J. J., & Kobourov, S. G. (2007). Characterization of unlabeled level planar trees. In Graph Drawing - 14th International Symposium, GD 2006, Revised Papers (pp. 367-379). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4372 LNCS).