[{"author":[{"last_name":"Aichholzer","full_name":"Aichholzer, Oswin","first_name":"Oswin"},{"last_name":"Obmann","full_name":"Obmann, Julia","first_name":"Julia"},{"last_name":"Patak","full_name":"Patak, Pavel","id":"B593B804-1035-11EA-B4F1-947645A5BB83","first_name":"Pavel"},{"first_name":"Daniel","full_name":"Perz, Daniel","last_name":"Perz"},{"full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","department":[{"_id":"KrCh"},{"_id":"UlWa"}],"title":"Disjoint tree-compatible plane perfect matchings","citation":{"chicago":"Aichholzer, Oswin, Julia Obmann, Pavel Patak, Daniel Perz, and Josef Tkadlec. “Disjoint Tree-Compatible Plane Perfect Matchings.” In 36th European Workshop on Computational Geometry, 2020.","ista":"Aichholzer O, Obmann J, Patak P, Perz D, Tkadlec J. 2020. Disjoint tree-compatible plane perfect matchings. 36th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 56.","mla":"Aichholzer, Oswin, et al. “Disjoint Tree-Compatible Plane Perfect Matchings.” 36th European Workshop on Computational Geometry, 56, 2020.","apa":"Aichholzer, O., Obmann, J., Patak, P., Perz, D., & Tkadlec, J. (2020). Disjoint tree-compatible plane perfect matchings. In 36th European Workshop on Computational Geometry. Würzburg, Germany, Virtual.","ama":"Aichholzer O, Obmann J, Patak P, Perz D, Tkadlec J. Disjoint tree-compatible plane perfect matchings. In: 36th European Workshop on Computational Geometry. ; 2020.","short":"O. Aichholzer, J. Obmann, P. Patak, D. Perz, J. Tkadlec, in:, 36th European Workshop on Computational Geometry, 2020.","ieee":"O. Aichholzer, J. Obmann, P. Patak, D. Perz, and J. Tkadlec, “Disjoint tree-compatible plane perfect matchings,” in 36th European Workshop on Computational Geometry, Würzburg, Germany, Virtual, 2020."},"date_updated":"2024-03-05T09:00:07Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","conference":{"name":"EuroCG: European Workshop on Computational Geometry","start_date":"2020-03-16","location":"Würzburg, Germany, Virtual","end_date":"2020-03-18"},"status":"public","_id":"15082","article_number":"56","date_published":"2020-04-01T00:00:00Z","date_created":"2024-03-05T08:57:17Z","year":"2020","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"36th European Workshop on Computational Geometry","quality_controlled":"1","main_file_link":[{"url":"https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/data/uploads/papers/eurocg20_paper_56.pdf","open_access":"1"}],"oa":1,"month":"04","abstract":[{"lang":"eng","text":"Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2.\r\nWe show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter\r\nof this graph is either 4 or 5, independent of n."}],"oa_version":"Published Version","acknowledgement":"Research on this work was initiated at the 6th Austrian-Japanese-Mexican-Spanish Workshop on Discrete Geometry and continued during the 16th European Geometric Graph-Week, both held near Strobl, Austria. We are grateful to the participants for the inspiring atmosphere. We especially thank Alexander Pilz for bringing this class of problems to our attention and Birgit Vogtenhuber for inspiring discussions. D.P. is partially supported by the FWF grant I 3340-N35 (Collaborative DACH project Arrangements and Drawings). The research stay of P.P. at IST Austria is funded by the project CZ.02.2.69/0.0/0.0/17_050/0008466 Improvement of internationalization in the field of research and development at Charles University, through the support of quality projects MSCA-IF. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922."},{"oa":1,"publisher":"ACM","quality_controlled":"1","publication":"Journal of the ACM","day":"01","year":"2019","isi":1,"date_created":"2019-11-26T10:13:59Z","date_published":"2019-06-01T00:00:00Z","doi":"10.1145/3314024","article_number":"21","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. Journal of the ACM. 2019;66(3). doi:10.1145/3314024","apa":"Goaoc, X., Patak, P., Patakova, Z., Tancer, M., & Wagner, U. (2019). Shellability is NP-complete. Journal of the ACM. ACM. https://doi.org/10.1145/3314024","short":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, U. Wagner, Journal of the ACM 66 (2019).","ieee":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” Journal of the ACM, vol. 66, no. 3. ACM, 2019.","mla":"Goaoc, Xavier, et al. “Shellability Is NP-Complete.” Journal of the ACM, vol. 66, no. 3, 21, ACM, 2019, doi:10.1145/3314024.","ista":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. 2019. Shellability is NP-complete. Journal of the ACM. 66(3), 21.","chicago":"Goaoc, Xavier, Pavel Patak, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete.” Journal of the ACM. ACM, 2019. https://doi.org/10.1145/3314024."},"title":"Shellability is NP-complete","article_processing_charge":"No","external_id":{"isi":["000495406300007"],"arxiv":["1711.08436"]},"author":[{"first_name":"Xavier","last_name":"Goaoc","full_name":"Goaoc, Xavier"},{"full_name":"Patak, Pavel","last_name":"Patak","id":"B593B804-1035-11EA-B4F1-947645A5BB83","first_name":"Pavel"},{"id":"48B57058-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","last_name":"Patakova","full_name":"Patakova, Zuzana","orcid":"0000-0002-3975-1683"},{"first_name":"Martin","full_name":"Tancer, Martin","last_name":"Tancer"},{"last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli"}],"oa_version":"Preprint","abstract":[{"text":"We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes. Another simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-shellable.","lang":"eng"}],"intvolume":" 66","month":"06","main_file_link":[{"url":"https://arxiv.org/pdf/1711.08436.pdf","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0004-5411"]},"issue":"3","related_material":{"record":[{"status":"public","id":"184","relation":"earlier_version"}]},"volume":66,"_id":"7108","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-09-06T11:10:58Z","department":[{"_id":"UlWa"}]}]