Extending partial representations of circle graphs

Steven Chaplick, Radoslav Fulek, Pavel Klavík*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation ' giving some predrawn chords that represent an induced subgraph of G. The question is whether one can extend ' to a representation of the entire graph G, that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of G. Our main result is an ( n3) time algorithm for partial representation extension of circle graphs, where n is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.

Original languageEnglish
Pages (from-to)365-394
Number of pages30
JournalJournal of Graph Theory
Issue number4
Publication statusPublished - Aug 2019
Externally publishedYes


  • algorithm
  • circle graphs
  • partial representation extension
  • recognition
  • split decomposition


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