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 pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend R' to a representation 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. © 2013 Springer International Publishing Switzerland.
CITATION STYLE
Chaplick, S., Fulek, R., & Klavík, P. (2013). Extending partial representations of circle graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8242 LNCS, pp. 131–142). Springer Verlag. https://doi.org/10.1007/978-3-319-03841-4_12
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