{"date_updated":"2023-09-27T12:14:49Z","main_file_link":[{"url":"https://arxiv.org/abs/1602.01346","open_access":"1"}],"_id":"794","publication":"Computational Geometry: Theory and Applications","doi":"10.1016/j.comgeo.2017.06.016","publist_id":"6860","acknowledgement":"I would like to thank Jan Kynčl, Dömötör Pálvölgyi and anonymous referees for many comments and suggestions that helped to improve the presentation of the result.","page":"1 - 13","publication_status":"published","external_id":{"isi":["000412039700001"]},"day":"01","publisher":"Elsevier","year":"2017","volume":66,"language":[{"iso":"eng"}],"oa":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1165"}]},"quality_controlled":"1","scopus_import":"1","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."}],"isi":1,"intvolume":"        66","citation":{"ista":"Fulek R. 2017. C-planarity of embedded cyclic c-graphs. Computational Geometry: Theory and Applications. 66, 1–13.","short":"R. Fulek, Computational Geometry: Theory and Applications 66 (2017) 1–13.","ama":"Fulek R. C-planarity of embedded cyclic c-graphs. <i>Computational Geometry: Theory and Applications</i>. 2017;66:1-13. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.016\">10.1016/j.comgeo.2017.06.016</a>","chicago":"Fulek, Radoslav. “C-Planarity of Embedded Cyclic c-Graphs.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.016\">https://doi.org/10.1016/j.comgeo.2017.06.016</a>.","ieee":"R. Fulek, “C-planarity of embedded cyclic c-graphs,” <i>Computational Geometry: Theory and Applications</i>, vol. 66. Elsevier, pp. 1–13, 2017.","apa":"Fulek, R. (2017). C-planarity of embedded cyclic c-graphs. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.016\">https://doi.org/10.1016/j.comgeo.2017.06.016</a>","mla":"Fulek, Radoslav. “C-Planarity of Embedded Cyclic c-Graphs.” <i>Computational Geometry: Theory and Applications</i>, vol. 66, Elsevier, 2017, pp. 1–13, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.016\">10.1016/j.comgeo.2017.06.016</a>."},"author":[{"last_name":"Fulek","full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","first_name":"Radoslav"}],"department":[{"_id":"UlWa"}],"status":"public","title":"C-planarity of embedded cyclic c-graphs","type":"journal_article","month":"12","date_published":"2017-12-01T00:00:00Z","date_created":"2018-12-11T11:48:32Z","oa_version":"Preprint","article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"}