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


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.


Boxicity Chordal bipartite graphs Interval graphs Grid intersection graphs 


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  1. 1.
    Brandstädt A.: Classes of bipartite graphs related to chordal graphs. Discrete Appl. Math. 32(1), 51–60 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Brandstädt A., Bang Le V., Spinrad J.P.: Graph Classes: A Survey. SIAM, Philadelphia (1999)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chandran L.S., Francis M.C., Sivadasan N.: Geometric representation of graphs in low dimension using axis parallel boxes. Algorithmica 56(2), 129–140 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Chandran L.S., Francis M.C., Sivadasan N.: Boxicity and maximum degree. J. Combinatorial Theory Ser. B 98(2), 443–445 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Chandran L.S., Sivadasan N.: Boxicity and treewidth. J. Combinatorial Theory Ser. B 97(5), 733–744 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Cozzens, M.B.: Higher and multidimensional analogues of interval graphs. PhD thesis, Rutgers University, New Brunswick (1981)Google Scholar
  7. 7.
    Cozzens M.B., Roberts F.S.: Computing the boxicity of a graph by covering its complement by cointerval graphs. Discrete Appl. Math. 6, 217–228 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Farber M.: Characterizations of strongly chordal graphs. Discrete Math. 43(2–3), 173–189 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Golumbic, M.C., Goss, C.F.: Perfect elimination and chordal bipartite graphs. J. Graph Theory 2 155–163 (1978)Google Scholar
  10. 10.
    Golumbic M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)zbMATHGoogle Scholar
  11. 11.
    Hartman I.B.-A., Newman I., Ziv R.: On grid intersection graphs. Discrete Math. 87(1), 41–52 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Otachi Y., Okamoto Y., Yamazaki K.: Relationships between the class of unit grid intersection graphs and other classes of bipartite graphs. Discrete Appl. Math. 155, 2383–2390 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Roberts, F.S.: The boxicity and cubicity of a graph. In: Recent Progresses in Combinatorics, pp. 301–310. Academic Press, New York (1969)Google Scholar
  14. 14.
    Scheinerman, E.R.: Intersection classes and multiple intersection parameters. PhD thesis, Princeton University, Princeton (1984)Google Scholar
  15. 15.
    Thomassen C.: Interval representations of planar graphs. J. Combinatorial Theory Ser. B 40, 9–20 (1986)CrossRefzbMATHMathSciNetGoogle Scholar

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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