@inproceedings{75781fdcdff8417eba8fef99403650f4,
title = "Extending Partial Representations of Circle Graphs",
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.keywordsintersection graphinterval graphchordal graphprime graphcircle graphthese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.",
author = "Steven Chaplick and Radoslav Fulek and Pavel Klav{\'i}k",
note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",
year = "2013",
doi = "10.1007/978-3-319-03841-4_12",
language = "English",
series = "Lecture Notes in Computer Science",
publisher = "Springer, Cham",
pages = "131--142",
editor = "S. Wismath and A. Wolff",
booktitle = "Graph Drawing. GD 2013",
address = "Switzerland",
}