Colored simultaneous geometric embeddings

U. Brandes, C. Erten, J. Fowler, F. Frati, M. Geyer, C. Gutwenger, S. Hong, M. Kaufmann, S. G. Kobourov, G. Liotta, P. Mutzel, A. Symvonis

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

11 Scopus citations

Abstract

We introduce the concept of concept simultaneous geometric embeddings as a generalization of simultaneous graph embeddings with and without mapping. We show that there exists a universal pointset of size n for paths colored with two or three colors. We use these results to show that colored simultaneous geometric embeddings exist for: (1) a 2-colored tree together with any number of 2-colored paths and (2) a 2-colored outerplanar graph together with any number of 2-colored paths. We also show that there does not exist a universal pointset of size n for paths colored with five colors. We finally show that the following simultaneous embeddings are not possible: (1) three 6-colored cycles, (2) four 6-colored paths, and (3) three 9-colored paths.

Original languageEnglish (US)
Title of host publicationComputing and Combinatorics - 13th Annual International Conference, COCOON 2007, Proceedings
PublisherSpringer-Verlag
Pages254-263
Number of pages10
ISBN (Print)9783540735441
DOIs
StatePublished - 2007
Event13th Annual International Computing and Combinatorics Conference, COCOON 2007 - Banff, Canada
Duration: Jul 16 2007Jul 19 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4598 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th Annual International Computing and Combinatorics Conference, COCOON 2007
CountryCanada
CityBanff
Period7/16/077/19/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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