Representing a cubic graph as the intersection graph of axisparallel boxes in three dimensions
Abstract
We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if their corresponding vertices are adjacent. In fact, we construct a representation in which any two intersecting boxes just touch at their boundaries. Further, this construction can be realized in linear time.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 arXiv:
 arXiv:1108.5635
 Bibcode:
 2011arXiv1108.5635A
 Keywords:

 Mathematics  Combinatorics