Colored point-set embeddings of acyclic graphs

Emilio Di Giacomo, Leszek Gasieniec, Giuseppe Liotta, Alfredo Navarra

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

2 Scopus citations

Abstract

We show that any planar drawing of a forest of three stars whose vertices are constrained to be at fixed vertex locations may require Ω(n2/3) edges each having Ω (n1/3) bends in the worst case. The lower bound holds even when the function that maps vertices to points is not a bijection but it is defined by a 3-coloring. In contrast, a constant number of bends per edge can be obtained for 3-colored paths and for 3-colored caterpillars whose leaves all have the same color. Such results answer to a long standing open problem.

Original languageEnglish (US)
Title of host publicationGraph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers
EditorsKwan-Liu Ma, Fabrizio Frati
PublisherSpringer Verlag
Pages413-425
Number of pages13
ISBN (Print)9783319739144
DOIs
StatePublished - Jan 1 2018
Externally publishedYes
Event25th International Symposium on Graph Drawing and Network Visualization, GD 2017 - Boston, United States
Duration: Sep 25 2017Sep 27 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10692 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Symposium on Graph Drawing and Network Visualization, GD 2017
CountryUnited States
CityBoston
Period9/25/179/27/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Di Giacomo, E., Gasieniec, L., Liotta, G., & Navarra, A. (2018). Colored point-set embeddings of acyclic graphs. In K-L. Ma, & F. Frati (Eds.), Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers (pp. 413-425). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10692 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-73915-1_32