Equilateral L-Contact Graphs

Steven Chaplick, Stephen G. Kobourov, Torsten Ueckerdt

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


We consider l-graphs, that is contact graphs of axis-aligned l-shapes in the plane, all with the same rotation. We provide several characterizations of l-graphs, drawing connections to schnyder realizers and canonical orders of maximally planar graphs. We show that every contact system of l’s can always be converted to an equivalent one with equilateral l’s. This can be used to show a stronger version of a result of thomassen, namely, that every planar graph can be represented as a contact system of square-based cuboids.we also study a slightly more restricted version of equilateral l-contact systems and show that these are equivalent to homothetic triangle contact representations of maximally planar graphs. We believe that this new interpretation of the problem might allow for efficient algorithms to find homothetic triangle contact representations, that do not use schramm’s monster packing theorem.keywordsplanar graphintersection graphouter faceedge labelcontact representationthese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science. WG 2013
EditorsA. Brandstädt, K. Jansen, R. Reischuk
Publication statusPublished - 2013
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

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