[{"volume":24,"ddc":["000"],"year":"2017","citation":{"ama":"Fulek R, Kynčl J, Pálvölgyi D. Unified Hanani Tutte theorem. <i>Electronic Journal of Combinatorics</i>. 2017;24(3). doi:<a href=\"https://doi.org/10.37236/6663\">10.37236/6663</a>","apa":"Fulek, R., Kynčl, J., &#38; Pálvölgyi, D. (2017). Unified Hanani Tutte theorem. <i>Electronic Journal of Combinatorics</i>. International Press. <a href=\"https://doi.org/10.37236/6663\">https://doi.org/10.37236/6663</a>","ieee":"R. Fulek, J. Kynčl, and D. Pálvölgyi, “Unified Hanani Tutte theorem,” <i>Electronic Journal of Combinatorics</i>, vol. 24, no. 3. International Press, 2017.","chicago":"Fulek, Radoslav, Jan Kynčl, and Dömötör Pálvölgyi. “Unified Hanani Tutte Theorem.” <i>Electronic Journal of Combinatorics</i>. International Press, 2017. <a href=\"https://doi.org/10.37236/6663\">https://doi.org/10.37236/6663</a>.","mla":"Fulek, Radoslav, et al. “Unified Hanani Tutte Theorem.” <i>Electronic Journal of Combinatorics</i>, vol. 24, no. 3, P3.18, International Press, 2017, doi:<a href=\"https://doi.org/10.37236/6663\">10.37236/6663</a>.","short":"R. Fulek, J. Kynčl, D. Pálvölgyi, Electronic Journal of Combinatorics 24 (2017).","ista":"Fulek R, Kynčl J, Pálvölgyi D. 2017. Unified Hanani Tutte theorem. Electronic Journal of Combinatorics. 24(3), P3.18."},"date_updated":"2022-03-18T12:58:53Z","day":"28","doi":"10.37236/6663","abstract":[{"lang":"eng","text":"We introduce a common generalization of the strong Hanani–Tutte theorem and the weak Hanani–Tutte theorem: if a graph G has a drawing D in the plane where every pair of independent edges crosses an even number of times, then G has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in D. The theorem is implicit in the proof of the strong Hanani–Tutte theorem by Pelsmajer, Schaefer and Štefankovič. We give a new, somewhat simpler proof."}],"ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:48:06Z","publisher":"International Press","article_type":"original","scopus_import":"1","_id":"795","issue":"3","author":[{"orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav","first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kynčl, Jan","first_name":"Jan","last_name":"Kynčl"},{"full_name":"Pálvölgyi, Dömötör","last_name":"Pálvölgyi","first_name":"Dömötör"}],"department":[{"_id":"UlWa"}],"article_processing_charge":"No","date_created":"2018-12-11T11:48:32Z","publication_status":"published","intvolume":"        24","title":"Unified Hanani Tutte theorem","file":[{"content_type":"application/pdf","file_name":"2017_ElectrCombi_Fulek.pdf","date_updated":"2020-07-14T12:48:06Z","file_size":236944,"checksum":"ef320cff0f062051e858f929be6a3581","date_created":"2019-01-18T14:04:08Z","creator":"dernst","file_id":"5853","access_level":"open_access","relation":"main_file"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_published":"2017-07-28T00:00:00Z","publication_identifier":{"issn":["10778926"]},"publist_id":"6859","oa":1,"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Electronic Journal of Combinatorics","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","article_number":"P3.18","month":"07"},{"ddc":["500"],"volume":24,"abstract":[{"lang":"eng","text":"A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2."}],"day":"14","year":"2017","citation":{"chicago":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” <i>The Electronic Journal of Combinatorics</i>. International Press, 2017.","ieee":"J. Kynčl and Z. Patakova, “On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4,” <i>The Electronic Journal of Combinatorics</i>, vol. 24, no. 3. International Press, pp. 1–44, 2017.","ama":"Kynčl J, Patakova Z. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. <i>The Electronic Journal of Combinatorics</i>. 2017;24(3):1-44.","apa":"Kynčl, J., &#38; Patakova, Z. (2017). On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. <i>The Electronic Journal of Combinatorics</i>. International Press.","ista":"Kynčl J, Patakova Z. 2017. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. 24(3), 1–44.","mla":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” <i>The Electronic Journal of Combinatorics</i>, vol. 24, no. 3, International Press, 2017, pp. 1–44.","short":"J. Kynčl, Z. Patakova, The Electronic Journal of Combinatorics 24 (2017) 1–44."},"date_updated":"2021-01-12T08:11:28Z","publisher":"International Press","file_date_updated":"2020-07-14T12:47:47Z","quality_controlled":"1","page":"1-44","intvolume":"        24","pubrep_id":"984","title":"On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4","department":[{"_id":"UlWa"}],"date_created":"2018-12-11T11:48:00Z","publication_status":"published","issue":"3","author":[{"full_name":"Kynčl, Jan","first_name":"Jan","last_name":"Kynčl"},{"first_name":"Zuzana","last_name":"Patakova","orcid":"0000-0002-3975-1683","full_name":"Patakova, Zuzana","id":"48B57058-F248-11E8-B48F-1D18A9856A87"}],"_id":"701","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_name":"IST-2018-984-v1+1_Patakova_on_the_nonexistence_of_k-reptile_simplices_in_R_3_and_R_4_2017.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:47:47Z","file_size":544042,"checksum":"a431e573e31df13bc0f66de3061006ec","date_created":"2018-12-12T10:14:25Z","creator":"system","file_id":"5077","relation":"main_file","access_level":"open_access"}],"oa":1,"publist_id":"6996","publication_identifier":{"issn":["10778926"]},"type":"journal_article","date_published":"2017-07-14T00:00:00Z","language":[{"iso":"eng"}],"month":"07","oa_version":"Submitted Version","has_accepted_license":"1","publication":"The Electronic Journal of Combinatorics"}]