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Separation Dimension of Graphs and Hypergraphs

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Abstract

Separation dimension of a hypergraph H, denoted by \(\pi (H)\), is the smallest natural number k so that the vertices of H can be embedded in \(\mathbb {R}^k\) such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension. In this paper, we study the separation dimension of hypergraphs and graphs.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology Karnataka, Surathkal, Mangalore, 575025, India

    Manu Basavaraju

  2. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, 560012, India

    L. Sunil Chandran

  3. Department of Computer Science, Caesarea Rothschild Institute, University of Haifa, 31905, Haifa, Israel

    Martin Charles Golumbic & Deepak Rajendraprasad

  4. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Rogers Mathew

Authors
  1. Manu Basavaraju
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  2. L. Sunil Chandran
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  3. Martin Charles Golumbic
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  4. Rogers Mathew
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  5. Deepak Rajendraprasad
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Corresponding author

Correspondence to Rogers Mathew.

Additional information

Rogers Mathew: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel. This work was done when the author was affiliated with the Department of Computer Science, Caesarea Rothschild Institute, University of Haifa, 31905 Haifa, Israel.

Deepak Rajendraprasad: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel and The Israel Science Foundation (Grant Number 862/10).

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Basavaraju, M., Chandran, L.S., Golumbic, M.C. et al. Separation Dimension of Graphs and Hypergraphs. Algorithmica 75, 187–204 (2016). https://doi.org/10.1007/s00453-015-0050-6

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  • DOI: https://doi.org/10.1007/s00453-015-0050-6

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