We introduce a concept of intersection dimension of a graph with respect to a graph class. This generalizes ferrers dimension, boxicity, and poset dimension, and leads to interesting new problems. We focus in particular on bipartite graph classes defined as intersection graphs of two kinds of geometric objects. We relate well-known graph classes such as interval bigraphs, two-directional orthogonal ray graphs, chain graphs, and (unit) grid intersection graphs with respect to these dimensions. As an application of these graph-theoretic results, we show that the recognition problems for certain graph classes are np-complete.keywordsferrers dimensionboxicityunit grid intersection graphsegment-ray graphsorthogonal ray graphnp-hardness.
|Title of host publication||Theory and Applications of Models of Computation. TAMC 2014|
|Editors||T.V. Gopal, M. Agrawal, A. Lia, S.B. Cooper|
|Publication status||Published - 2014|
|Series||Lecture Notes in Computer Science|