{"project":[{"call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"volume":"9801 ","date_updated":"2023-09-27T12:14:48Z","abstract":[{"lang":"eng","text":"We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle."}],"status":"public","day":"08","quality_controlled":"1","acknowledgement":"R. Fulek—The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no [291734].\r\nI would like to thank Jan Kynčl and Dömötör Pálvölgyi for many comments and suggestions that helped to improve the presentation of the result.","main_file_link":[{"url":"https://arxiv.org/abs/1602.01346","open_access":"1"}],"related_material":{"record":[{"status":"public","id":"794","relation":"later_version"}]},"ec_funded":1,"publisher":"Springer","scopus_import":1,"oa":1,"conference":{"location":"Athens, Greece","start_date":"2016-09-19","end_date":"2016-09-21","name":"GD: Graph Drawing and Network Visualization"},"publication_status":"published","_id":"1165","doi":"10.1007/978-3-319-50106-2_8","month":"12","title":"C-planarity of embedded cyclic c-graphs","oa_version":"Preprint","type":"conference","citation":{"short":"R. Fulek, in:, Springer, 2016, pp. 94–106.","apa":"Fulek, R. (2016). C-planarity of embedded cyclic c-graphs (Vol. 9801, pp. 94–106). Presented at the GD: Graph Drawing and Network Visualization, Athens, Greece: Springer. <a href=\"https://doi.org/10.1007/978-3-319-50106-2_8\">https://doi.org/10.1007/978-3-319-50106-2_8</a>","ista":"Fulek R. 2016. C-planarity of embedded cyclic c-graphs. GD: Graph Drawing and Network Visualization, LNCS, vol. 9801, 94–106.","ama":"Fulek R. C-planarity of embedded cyclic c-graphs. In: Vol 9801. Springer; 2016:94-106. doi:<a href=\"https://doi.org/10.1007/978-3-319-50106-2_8\">10.1007/978-3-319-50106-2_8</a>","chicago":"Fulek, Radoslav. “C-Planarity of Embedded Cyclic c-Graphs,” 9801:94–106. Springer, 2016. <a href=\"https://doi.org/10.1007/978-3-319-50106-2_8\">https://doi.org/10.1007/978-3-319-50106-2_8</a>.","mla":"Fulek, Radoslav. <i>C-Planarity of Embedded Cyclic c-Graphs</i>. Vol. 9801, Springer, 2016, pp. 94–106, doi:<a href=\"https://doi.org/10.1007/978-3-319-50106-2_8\">10.1007/978-3-319-50106-2_8</a>.","ieee":"R. Fulek, “C-planarity of embedded cyclic c-graphs,” presented at the GD: Graph Drawing and Network Visualization, Athens, Greece, 2016, vol. 9801, pp. 94–106."},"alternative_title":["LNCS"],"date_created":"2018-12-11T11:50:30Z","year":"2016","date_published":"2016-12-08T00:00:00Z","language":[{"iso":"eng"}],"author":[{"full_name":"Fulek, Radoslav","orcid":"0000-0001-8485-1774","first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6192","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"94 - 106","department":[{"_id":"UlWa"}]}