{"day":"09","quality_controlled":"1","intvolume":"      9843","date_updated":"2021-01-12T06:50:03Z","status":"public","abstract":[{"text":"A drawing in the plane (ℝ2) of a graph G = (V,E) equipped with a function γ : V → ℕ is x-bounded if (i) x(u) &lt; x(v) whenever γ(u) &lt; γ(v) and (ii) γ(u) ≤ γ(w) ≤ γ(v), where uv ∈ E and γ(u) ≤ γ(v), whenever x(w) ∈ x(uv), where x(.) denotes the projection to the xaxis.We prove a characterization of isotopy classes of embeddings of connected graphs equipped with γ in the plane containing an x-bounded embedding.Then we present an efficient algorithm, which relies on our result, for testing the existence of an x-bounded embedding if the given graph is a forest.This partially answers a question raised recently by Angelini et al.and Chang et al., and proves that c-planarity testing of flat clustered graphs with three clusters is tractable when the underlying abstract graph is a forest.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1610.07144","open_access":"1"}],"ec_funded":1,"volume":9843,"project":[{"grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"year":"2016","date_published":"2016-08-09T00:00:00Z","alternative_title":["LNCS"],"date_created":"2018-12-11T11:51:31Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"31 - 42","department":[{"_id":"UlWa"}],"language":[{"iso":"eng"}],"publist_id":"5901","author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek","full_name":"Fulek, Radoslav","first_name":"Radoslav","orcid":"0000-0001-8485-1774"}],"conference":{"name":"IWOCA: International Workshop on Combinatorial Algorithms","end_date":"2018-08-19","location":"Helsinki, Finland","start_date":"2016-08-17"},"publication_status":"published","publisher":"Springer","scopus_import":1,"oa":1,"oa_version":"Preprint","citation":{"ieee":"R. Fulek, “Bounded embeddings of graphs in the plane,” presented at the IWOCA: International Workshop on Combinatorial Algorithms, Helsinki, Finland, 2016, vol. 9843, pp. 31–42.","mla":"Fulek, Radoslav. <i>Bounded Embeddings of Graphs in the Plane</i>. Vol. 9843, Springer, 2016, pp. 31–42, doi:<a href=\"https://doi.org/10.1007/978-3-319-44543-4_3\">10.1007/978-3-319-44543-4_3</a>.","chicago":"Fulek, Radoslav. “Bounded Embeddings of Graphs in the Plane,” 9843:31–42. Springer, 2016. <a href=\"https://doi.org/10.1007/978-3-319-44543-4_3\">https://doi.org/10.1007/978-3-319-44543-4_3</a>.","ista":"Fulek R. 2016. Bounded embeddings of graphs in the plane. IWOCA: International Workshop on Combinatorial Algorithms, LNCS, vol. 9843, 31–42.","ama":"Fulek R. Bounded embeddings of graphs in the plane. In: Vol 9843. Springer; 2016:31-42. doi:<a href=\"https://doi.org/10.1007/978-3-319-44543-4_3\">10.1007/978-3-319-44543-4_3</a>","apa":"Fulek, R. (2016). Bounded embeddings of graphs in the plane (Vol. 9843, pp. 31–42). Presented at the IWOCA: International Workshop on Combinatorial Algorithms, Helsinki, Finland: Springer. <a href=\"https://doi.org/10.1007/978-3-319-44543-4_3\">https://doi.org/10.1007/978-3-319-44543-4_3</a>","short":"R. Fulek, in:, Springer, 2016, pp. 31–42."},"type":"conference","_id":"1348","doi":"10.1007/978-3-319-44543-4_3","month":"08","title":"Bounded embeddings of graphs in the plane"}