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Graphs and Combinatorics

, Volume 27, Issue 3, pp 353–362 | Cite as

Chordal Bipartite Graphs with High Boxicity

  • L. Sunil ChandranEmail author
  • Mathew C. Francis
  • Rogers Mathew
Proceedings Paper

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.

Keywords

Boxicity Chordal bipartite graphs Interval graphs Grid intersection graphs 

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Copyright information

© Springer 2011

Authors and Affiliations

  • L. Sunil Chandran
    • 1
    Email author
  • Mathew C. Francis
    • 1
  • Rogers Mathew
    • 1
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

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