Extending Partial Representations of Proper and Unit Interval Graphs

  title={Extending Partial Representations of Proper and Unit Interval Graphs},
  author={Pavel Klav{\'i}k and Jan Kratochv{\'i}l and Yota Otachi and Ignaz Rutter and Toshiki Saitoh and Maria Saumell and Tom{\'a}s Vyskocil},
The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire graph. In this paper, we give a linear-time algorithm for extending proper interval representations and an almost quadratic-time algorithm for extending unit interval representations. We also introduce the more general problem of bounded representations of unit… CONTINUE READING