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Intersection Dimension of Bipartite Graphs

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Theory and Applications of Models of Computation (TAMC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8402))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague, Czech Republic

    Steven Chaplick

  2. School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada, V5A 1S6

    Pavol Hell

  3. School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa, 923-1292, Japan

    Yota Otachi & Ryuhei Uehara

  4. Graduate School of Engineering, Kobe University, Rokkodai 1-1, Nada, Kobe, 657-8501, Japan

    Toshiki Saitoh

Authors
  1. Steven Chaplick
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  2. Pavol Hell
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  3. Yota Otachi
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  4. Toshiki Saitoh
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  5. Ryuhei Uehara
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, College of Engineering, Anna University, Chennai, 600 025, Chennai, India

    T. V. Gopal

  2. Department of Computer Science and Engineering, Indian Institute of Technology, 208016, Kanpur, India

    Manindra Agrawal

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Zhongguancun, Haidian District, 100190, Beijing, China

    Angsheng Li

  4. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

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Chaplick, S., Hell, P., Otachi, Y., Saitoh, T., Uehara, R. (2014). Intersection Dimension of Bipartite Graphs. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2014. Lecture Notes in Computer Science, vol 8402. Springer, Cham. https://doi.org/10.1007/978-3-319-06089-7_23

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  • DOI: https://doi.org/10.1007/978-3-319-06089-7_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06088-0

  • Online ISBN: 978-3-319-06089-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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