We study two variants of the problem of contact representation of planar graphs with axis-aligned boxes. In a cube-contact representation we realize each vertex with a cube, while in a proportional box-contact representation each vertex is an axis-aligned box with a prespecified volume. We present algorithms for constructing cube-contact representation and proportional box-contact representation for several classes of planar graphs.
@article{arxiv.1510.02484,
title = {On Contact Graphs with Cubes and Proportional Boxes},
author = {Md. Jawaherul Alam and Michael Kaufmann and Stephen G. Kobourov},
journal= {arXiv preprint arXiv:1510.02484},
year = {2015}
}