@article{5790,
  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 R′ giving some predrawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R 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 O(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.},
  author       = {Chaplick, Steven and Fulek, Radoslav and Klavík, Pavel},
  issn         = {03649024},
  journal      = {Journal of Graph Theory},
  number       = {4},
  pages        = {365--394},
  publisher    = {Wiley},
  title        = {{Extending partial representations of circle graphs}},
  doi          = {10.1002/jgt.22436},
  volume       = {91},
  year         = {2019},
}