TY - JOUR
AB - 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.
AU - Chaplick, Steven
AU - Fulek, Radoslav
AU - Klavík, Pavel
ID - 5790
IS - 4
JF - Journal of Graph Theory
SN - 03649024
TI - Extending partial representations of circle graphs
VL - 91
ER -