Chordal Bipartite Graphs with High Boxicity

  • Authors:

  • L. Sunil Chandran;Mathew C. Francis;Rogers Mathew

  • Affiliations:

  • Indian Institute of Science, Department of Computer Science and Automation, 560012, Bangalore, India;Indian Institute of Science, Department of Computer Science and Automation, 560012, Bangalore, India;Indian Institute of Science, Department of Computer Science and Automation, 560012, Bangalore, India

  • Venue:
  • Graphs and Combinatorics - The Japan Conference on Computational Geometry and Graphs (JCCGG2009)
  • Year:
  • 2011

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Abstract

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.