Extending Partial Representations of Circle GraphsChaplick, Steven and Fulek, Radoslav and Klavík, Pavel (2013) Extending Partial Representations of Circle Graphs. In: 21st International Symposium, GD 2013, September 2325, 2013 , pp. 131142(Official URL: http://dx.doi.org/10.1007/9783319038414_12). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319038414_12
AbstractThe 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 G, i.e., whether one can draw the remaining chords into a partially predrawn representation. Our main result is a polynomialtime 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.
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