Monotone Proper Interval Digraphs and Min-Max Orderings

@article{Hell2012MonotonePI,
  title={Monotone Proper Interval Digraphs and Min-Max Orderings},
  author={Pavol Hell and Arash Rafiey},
  journal={SIAM J. Discrete Math.},
  year={2012},
  volume={26},
  pages={1576-1596}
}
We introduce a class of digraphs analogous to proper interval graphs and bigraphs. They are defined via a geometric representation by two inclusion-free families of intervals satisfying a certain monotonicity condition; hence we call them monotone proper interval digraphs. They admit a number of equivalent definitions, including an ordering characterization by so-called MinMax orderings, and the existence of certain graph polymorphisms. Min-Max orderings arose in the study of minimum cost… CONTINUE READING

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