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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.DM2018
Dushnik-Miller dimension of TD-Delaunay complexes
Daniel Gonçalves, Lucas Isenmann
TD-Delaunay graphs, where TD stands for triangular distance, is a variation of the classical Delaunay triangulations obtained from a specific convex distance function. Bonichon et.…