[{"article_processing_charge":"No","page":"359-371","status":"public","abstract":[{"lang":"eng","text":"We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on   n>1  vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and   m>4n  edges is larger than   cm2n  for some constant   c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and   m⟶∞ ."}],"publication_status":"published","intvolume":"     12590","main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"volume":12590,"series_title":"LNCS","department":[{"_id":"HeEd"}],"arxiv":1,"title":"Crossings between non-homotopic edges","scopus_import":"1","year":"2020","publication":"28th International Symposium on Graph Drawing and Network Visualization","day":"20","acknowledgement":"Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908.","citation":{"ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: <i>28th International Symposium on Graph Drawing and Network Visualization</i>. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>","ista":"Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.","chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In <i>28th International Symposium on Graph Drawing and Network Visualization</i>, 12590:359–71. LNCS. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>.","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” <i>28th International Symposium on Graph Drawing and Network Visualization</i>, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>.","apa":"Pach, J., Tardos, G., &#38; Tóth, G. (2020). Crossings between non-homotopic edges. In <i>28th International Symposium on Graph Drawing and Network Visualization</i> (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in <i>28th International Symposium on Graph Drawing and Network Visualization</i>, Virtual, Online, 2020, vol. 12590, pp. 359–371."},"author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"Gábor","full_name":"Tardos, Gábor","last_name":"Tardos"},{"last_name":"Tóth","first_name":"Géza","full_name":"Tóth, Géza"}],"_id":"9299","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_updated":"2025-04-15T07:16:52Z","doi":"10.1007/978-3-030-68766-3_28","conference":{"end_date":"2020-09-18","location":"Virtual, Online","start_date":"2020-09-16","name":"GD: Graph Drawing and Network Visualization"},"type":"conference","language":[{"iso":"eng"}],"date_published":"2020-09-20T00:00:00Z","publisher":"Springer Nature","oa_version":"Preprint","date_created":"2021-03-28T22:01:44Z","month":"09","project":[{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"}],"publication_identifier":{"isbn":["9783030687656"],"eissn":["1611-3349"],"issn":["0302-9743"]},"external_id":{"arxiv":["2006.14908"]}}]