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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  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 thedoi:10.1016/0012-365x(90)90151-7 fatcat:xuhjleebljd53gcfs5i2f62r6a