Intersection Dimension of Bipartite Graphs

Steven Chaplick, Pavol Hell, Yota Otachi, Toshiki Saitoh, Ryuhei Uehara

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


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.
Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation. TAMC 2014
EditorsT.V. Gopal, M. Agrawal, A. Lia, S.B. Cooper
Publication statusPublished - 2014
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

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