Chaplick, Steven; Hell, Pavol; Otachi, Yota; Saitoh, Toshiki; Uehara, Ryuhei Intersection dimension of bipartite graphs. (English) Zbl 1406.05084 Gopal, T. V. (ed.) et al., Theory and applications of models of computation. 11th annual conference, TAMC 2014, Chennai, India, April 11–13, 2014. Proceedings. Berlin: Springer (ISBN 978-3-319-06088-0/pbk). Lecture Notes in Computer Science 8402, 323-340 (2014). Summary: 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.For the entire collection see [Zbl 1284.68014]. Cited in 4 Documents MSC: 05C75 Structural characterization of families of graphs 05C62 Graph representations (geometric and intersection representations, etc.) 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Keywords:Ferrers dimension; boxicity; unit grid intersection graph; segment-ray graphs; orthogonal ray graph; NP-hardness PDFBibTeX XMLCite \textit{S. Chaplick} et al., Lect. Notes Comput. Sci. 8402, 323--340 (2014; Zbl 1406.05084) Full Text: DOI