The Roberts characterization of proper and unit interval graphs

  title={The Roberts characterization of proper and unit interval graphs},
  author={Fr{\'e}d{\'e}ric Gardi},
  journal={Discrete Mathematics},
In this note, a constructive proof that the classes of proper interval graphs and unit interval graphs coincide is given, a result originally established by Fred S. Roberts. Additionally, the proof yields a linear-time and space algorithm to compute a unit interval representation, given a proper interval graph as input. © 2007 Elsevier B.V. All rights reserved. 

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Indifference graphs

  • F. S. Roberts
  • in: F. Harary (Ed.), Proof Techniques in Graph…
  • 1969
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Representations of indifference relations

  • F. S. Roberts
  • Ph.D. Thesis, Stanford University, Stanford, CA
  • 1968
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Optimal greedy algorithms for indifference graphs

  • P. J. Looges, S. Olariu
  • Comput. Math. Appl. 25
  • 1993

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