3 papers
cs.DM2019
Homothetic triangle representations of planar graphs
Daniel Gonçalves, Benjamin Lévêque, Alexandre Pinlou
We prove that every planar graph is the intersection graph of homothetic triangles in the plane.
cs.DM2018
Dushnik-Miller dimension of d-dimensional tilings with boxes
Mathew C. Francis, Daniel Gonçalves
Planar graphs are the graphs with Dushnik-Miller dimension at most three (W. Schnyder, Planar graphs and poset dimension, Order 5, 323-343, 1989). Consider the intersection graph o…
cs.CG2017
Planar graphs as L-intersection or L-contact graphs
Daniel Gonçalves, Lucas Isenmann, Claire Pennarun
The L-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel shapes in the plane. A subfamily of these graphs are {L, |, --}-contact…