Contact representations of graphs in 3D

Jawaherul Alam, William Evans, Stephen Kobourov, Sergey Pupyrev, Jackson Toeniskoetter, Torsten Ueckerdt

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

7 Scopus citations


We study contact representations of non-planar graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We present a liner-time algorithm constructing a representation of a 3-connected planar graph, its dual, and the vertex-face incidence graph with 3D boxes. We then investigate contact representations of 1- planar graphs. We first prove that optimal 1-planar graphs without separating 4-cycles admit a contact representation with 3D boxes. However, since not every optimal 1-planar graph can be represented in this way, we also consider contact representations with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a quadratic-time algorithm for representing optimal 1-planar graphs with L-shapes.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Ulrike Stege
Number of pages14
ISBN (Print)9783319218397
StatePublished - 2015
Event14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada
Duration: Aug 5 2015Aug 7 2015

Publication series

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


Other14th International Symposium on Algorithms and Data Structures, WADS 2015

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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