Chaplick, Steven; Fulek, RadoslavIST Austria ; Klavík, Pavel
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.
Journal of Graph Theory
Chaplick S, Fulek R, Klavík P. Extending partial representations of circle graphs. Journal of Graph Theory. 2019;91(4):365-394. doi:10.1002/jgt.22436
Chaplick, S., Fulek, R., & Klavík, P. (2019). Extending partial representations of circle graphs. Journal of Graph Theory, 91(4), 365–394. https://doi.org/10.1002/jgt.22436
Chaplick, Steven, Radoslav Fulek, and Pavel Klavík. “Extending Partial Representations of Circle Graphs.” Journal of Graph Theory 91, no. 4 (2019): 365–94. https://doi.org/10.1002/jgt.22436.
S. Chaplick, R. Fulek, and P. Klavík, “Extending partial representations of circle graphs,” Journal of Graph Theory, vol. 91, no. 4, pp. 365–394, 2019.
Chaplick S, Fulek R, Klavík P. 2019. Extending partial representations of circle graphs. Journal of Graph Theory. 91(4), 365–394.
Chaplick, Steven, et al. “Extending Partial Representations of Circle Graphs.” Journal of Graph Theory, vol. 91, no. 4, Wiley, 2019, pp. 365–94, doi:10.1002/jgt.22436.