TY - GEN
T1 - Equilateral L-Contact Graphs
AU - Chaplick, Steven
AU - Kobourov, Stephen G.
AU - Ueckerdt, Torsten
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-642-45043-3_13
DO - 10.1007/978-3-642-45043-3_13
M3 - Conference article in proceeding
T3 - Lecture Notes in Computer Science
SP - 139
EP - 151
BT - Graph-Theoretic Concepts in Computer Science. WG 2013
A2 - Brandstädt, A.
A2 - Jansen, K.
A2 - Reischuk, R.
ER -