[{"issue":"2","publication":"Combinatorica","page":"283-305","intvolume":"        40","status":"public","day":"01","type":"journal_article","date_created":"2021-06-22T06:42:26Z","publisher":"Springer","scopus_import":"1","language":[{"iso":"eng"}],"month":"04","date_published":"2020-04-01T00:00:00Z","article_type":"original","_id":"9582","extern":"1","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","quality_controlled":"1","oa_version":"Preprint","arxiv":1,"oa":1,"date_updated":"2023-02-23T14:01:45Z","volume":40,"article_processing_charge":"No","abstract":[{"lang":"eng","text":"The problem of finding dense induced bipartite subgraphs in H-free graphs has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer. In this paper, we obtain several results in this direction. First we prove that any H-free graph with minimum degree at least d contains an induced bipartite subgraph of minimum degree at least cH log d/log log d, thus nearly confirming one and proving another conjecture of Esperet, Kang and Thomassé. Complementing this result, we further obtain optimal bounds for this problem in the case of dense triangle-free graphs, and we also answer a question of Erdœs, Janson, Łuczak and Spencer."}],"author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","last_name":"Kwan","first_name":"Matthew Alan"},{"last_name":"Letzter","full_name":"Letzter, Shoham","first_name":"Shoham"},{"full_name":"Sudakov, Benny","last_name":"Sudakov","first_name":"Benny"},{"last_name":"Tran","full_name":"Tran, Tuan","first_name":"Tuan"}],"publication_status":"published","citation":{"ieee":"M. A. Kwan, S. Letzter, B. Sudakov, and T. Tran, “Dense induced bipartite subgraphs in triangle-free graphs,” <i>Combinatorica</i>, vol. 40, no. 2. Springer, pp. 283–305, 2020.","apa":"Kwan, M. A., Letzter, S., Sudakov, B., &#38; Tran, T. (2020). Dense induced bipartite subgraphs in triangle-free graphs. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/s00493-019-4086-0\">https://doi.org/10.1007/s00493-019-4086-0</a>","chicago":"Kwan, Matthew Alan, Shoham Letzter, Benny Sudakov, and Tuan Tran. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” <i>Combinatorica</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00493-019-4086-0\">https://doi.org/10.1007/s00493-019-4086-0</a>.","mla":"Kwan, Matthew Alan, et al. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” <i>Combinatorica</i>, vol. 40, no. 2, Springer, 2020, pp. 283–305, doi:<a href=\"https://doi.org/10.1007/s00493-019-4086-0\">10.1007/s00493-019-4086-0</a>.","ama":"Kwan MA, Letzter S, Sudakov B, Tran T. Dense induced bipartite subgraphs in triangle-free graphs. <i>Combinatorica</i>. 2020;40(2):283-305. doi:<a href=\"https://doi.org/10.1007/s00493-019-4086-0\">10.1007/s00493-019-4086-0</a>","ista":"Kwan MA, Letzter S, Sudakov B, Tran T. 2020. Dense induced bipartite subgraphs in triangle-free graphs. Combinatorica. 40(2), 283–305.","short":"M.A. Kwan, S. Letzter, B. Sudakov, T. Tran, Combinatorica 40 (2020) 283–305."},"main_file_link":[{"url":"https://arxiv.org/abs/1810.12144","open_access":"1"}],"external_id":{"arxiv":["1810.12144"]},"title":"Dense induced bipartite subgraphs in triangle-free graphs","doi":"10.1007/s00493-019-4086-0","year":"2020"},{"main_file_link":[{"url":"https://arxiv.org/abs/1709.00508","open_access":"1"}],"isi":1,"external_id":{"isi":["000493267200003"],"arxiv":["1709.00508"]},"title":"Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4","year":"2019","doi":"10.1007/s00493-019-3905-7","ec_funded":1,"_id":"7034","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","oa_version":"Preprint","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"},{"grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425","name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF"}],"arxiv":1,"volume":39,"oa":1,"date_updated":"2023-08-30T07:26:25Z","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani–Tutte theorem cannot be extended to the orientable surface of genus 4. As a base step in the construction we use a counterexample to an extension of the unified Hanani–Tutte theorem on the torus."}],"author":[{"last_name":"Fulek","full_name":"Fulek, Radoslav","orcid":"0000-0001-8485-1774","first_name":"Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kynčl, Jan","last_name":"Kynčl","first_name":"Jan"}],"publication_status":"published","citation":{"chicago":"Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” <i>Combinatorica</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00493-019-3905-7\">https://doi.org/10.1007/s00493-019-3905-7</a>.","ieee":"R. Fulek and J. Kynčl, “Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4,” <i>Combinatorica</i>, vol. 39, no. 6. Springer Nature, pp. 1267–1279, 2019.","apa":"Fulek, R., &#38; Kynčl, J. (2019). Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-019-3905-7\">https://doi.org/10.1007/s00493-019-3905-7</a>","ista":"Fulek R, Kynčl J. 2019. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 39(6), 1267–1279.","short":"R. Fulek, J. Kynčl, Combinatorica 39 (2019) 1267–1279.","mla":"Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” <i>Combinatorica</i>, vol. 39, no. 6, Springer Nature, 2019, pp. 1267–79, doi:<a href=\"https://doi.org/10.1007/s00493-019-3905-7\">10.1007/s00493-019-3905-7</a>.","ama":"Fulek R, Kynčl J. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. <i>Combinatorica</i>. 2019;39(6):1267-1279. doi:<a href=\"https://doi.org/10.1007/s00493-019-3905-7\">10.1007/s00493-019-3905-7</a>"},"date_created":"2019-11-18T14:29:50Z","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","scopus_import":"1","language":[{"iso":"eng"}],"month":"10","article_type":"original","date_published":"2019-10-29T00:00:00Z","issue":"6","publication":"Combinatorica","page":"1267-1279","intvolume":"        39","status":"public","day":"29","type":"journal_article"},{"publication_status":"published","citation":{"ista":"Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260.","short":"H. Edelsbrunner, Combinatorica 10 (1990) 251–260.","mla":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>.","ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. 1990;10(3):251-260. doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>","chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>.","apa":"Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>","ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” <i>Combinatorica</i>, vol. 10, no. 3. Springer, pp. 251–260, 1990."},"abstract":[{"text":"Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.","lang":"eng"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert"}],"volume":10,"date_updated":"2022-02-21T11:08:30Z","publist_id":"2050","article_processing_charge":"No","_id":"4069","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"extern":"1","acknowledgement":"Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565.","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","oa_version":"None","quality_controlled":"1","year":"1990","doi":"10.1007/BF02122779","title":"An acyclicity theorem for cell complexes in d dimension","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02122779"}],"day":"01","type":"journal_article","intvolume":"        10","status":"public","issue":"3","publication":"Combinatorica","page":"251 - 260","month":"09","date_published":"1990-09-01T00:00:00Z","article_type":"original","publisher":"Springer","scopus_import":"1","language":[{"iso":"eng"}],"date_created":"2018-12-11T12:06:45Z"}]