Representing a cubic graph as the intersection graph of axis-parallel boxes in three dimensions

Details Representing a cubic graph as the intersection graph of axis-parallel boxes in three dimensions Representing a cubic graph as the intersection graph of axis-parallel boxes in three dimensions

2011-08-29

arxiv.org/abs/1108.5635v1

Mathematics

Combinatorics

Scientific paper

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.

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