The interval constrained 3-coloring problem

Jaroslaw Byrka, Andreas Karrenbauer, Laura Sanità

Research output: Contribution to journalArticleAcademicpeer-review


In this paper, we settle the open complexity status of interval constrained coloring with a fixed number of colors. We prove that the problem is already NP-complete if the number of different colors is 3. Previously, it has only been known that it is NP-complete, if the number of colors is part of the input and that the problem is solvable in polynomial time, if the number of colors is at most 2. We also show that it is hard to satisfy almost all of the constraints for a feasible instance (even in the restricted case where each interval is used at most once). This implies APX-hardness of maximizing the number of simultaneously satisfiable intervals.

Original languageEnglish
Pages (from-to)42-50
Number of pages9
JournalTheoretical Computer Science
Publication statusPublished - 16 Aug 2015
Externally publishedYes


  • APX-hardness
  • Interval constrained coloring

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