Dotted interval graphs

Yonatan Aumann, Moshe Lewenstein, Oren Melamud, Ron Pinter, Zohar Yakhini

Research output: Contribution to journalArticlepeer-review


We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG, but that DIGd graphs, that is, DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG d graphs is NP-complete even for d = 2. For any fixed d, we provide a 5/6d + o(d) approximation for the coloring of DIG d graphs. Finally, we show that finding the maximal clique in DIG d graphs is fixed parameter tractable in d.

Original languageEnglish
Article number9
JournalACM Transactions on Algorithms
Issue number2
StatePublished - Apr 2012


  • Approximation algorithms
  • Circular arc graph
  • Graph coloring
  • Graph theory
  • Intersection graph
  • Interval graph

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


Dive into the research topics of 'Dotted interval graphs'. Together they form a unique fingerprint.

Cite this