Extending Partial Representations of Circle Graphs

  • Steven Chaplick
  • Radoslav Fulek
  • Pavel Klavík
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

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 \(\mathcal{R'}\) giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend \(\mathcal{R'}\) to a representation \(\mathcal{R}\) of the entire G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation.

Our main result is a polynomial-time algorithm for partial representation extension of circle graphs. To show this, we describe the structure of all representation a circle graph based on split decomposition. This can be of an independent interest.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Steven Chaplick
    • 1
  • Radoslav Fulek
    • 1
  • Pavel Klavík
    • 2
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Computer Science Institute, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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