{"scopus_import":1,"oa_version":"Preprint","article_processing_charge":"No","publication":"Journal of Graph Theory","day":"01","doi":"10.1002/jgt.22436","quality_controlled":"1","date_published":"2019-08-01T00:00:00Z","oa":1,"abstract":[{"text":"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.","lang":"eng"}],"citation":{"ista":"Chaplick S, Fulek R, Klavík P. 2019. Extending partial representations of circle graphs. Journal of Graph Theory. 91(4), 365–394.","ama":"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","ieee":"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.","apa":"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","mla":"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.","chicago":"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.","short":"S. Chaplick, R. Fulek, P. Klavík, Journal of Graph Theory 91 (2019) 365–394."},"year":"2019","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1309.2399"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","title":"Extending partial representations of circle graphs","date_created":"2018-12-30T22:59:15Z","month":"08","intvolume":" 91","external_id":{"arxiv":["1309.2399"]},"publication_status":"published","department":[{"_id":"UlWa"}],"article_type":"original","date_updated":"2020-08-11T10:10:24Z","author":[{"full_name":"Chaplick, Steven","first_name":"Steven","last_name":"Chaplick"},{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek","orcid":"0000-0001-8485-1774","first_name":"Radoslav","full_name":"Fulek, Radoslav"},{"full_name":"Klavík, Pavel","first_name":"Pavel","last_name":"Klavík"}],"issue":"4","publisher":"Wiley","_id":"5790","project":[{"grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","publication_identifier":{"issn":["03649024"]},"volume":91,"page":"365-394","language":[{"iso":"eng"}],"status":"public","ec_funded":1}