Characterization of the graphs with boxicity ⩽2

Martin Quest, Gerd Wegner
1990 Discrete Mathematics  
The intersection graph of a family 8TI of sets has the sets in %' as vertices and an edge between two sets iff they have nonempty intersection. Following Roberts [4] the boxicity b(G) of a graph G is defined as the smallest d such that G is the intersection graph of boxes in Euclidean d-space, i.e. parallelepipeds with edges parallel to the coordinate axes. In this paper we will give a combinatorial characterization of the graphs with b(G)s2, called boxicity 2-graphs, by means of the
more » ... of zeros and ones in special matrices attached to the graph.
doi:10.1016/0012-365x(90)90151-7 fatcat:xuhjleebljd53gcfs5i2f62r6a