{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T01:06:12Z","timestamp":1766365572012,"version":"3.48.0"},"publisher-location":"Cham","reference-count":10,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030929305"},{"type":"electronic","value":"9783030929312"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-92931-2_16","type":"book-chapter","created":{"date-parts":[[2021,12,22]],"date-time":"2021-12-22T11:14:17Z","timestamp":1640171657000},"page":"223-227","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the\u00a0Number of\u00a0Edges of\u00a0Separated Multigraphs"],"prefix":"10.1007","author":[{"given":"Jacob","family":"Fox","sequence":"first","affiliation":[]},{"given":"J\u00e1nos","family":"Pach","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Suk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,23]]},"reference":[{"key":"16_CR1","doi-asserted-by":"crossref","unstructured":"Ajtai, M., Chv\u00e1tal, V., Newborn, M., Szemer\u00e9di, E.: Crossing-free subgraphs. In: North-Holland Mathematics Studies, vol. 60, pp. 9\u201312 (1982)","DOI":"10.1016\/S0304-0208(08)73484-4"},{"key":"16_CR2","doi-asserted-by":"publisher","first-page":"155","DOI":"10.4007\/annals.2015.181.1.2","volume":"181","author":"L Guth","year":"2015","unstructured":"Guth, L., Katz, N.H.: On the erd\u0151s distinct distances problem in the plane. Ann. Math. 181, 155\u2013190 (2015)","journal-title":"Ann. Math."},{"key":"16_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1007\/978-3-030-04414-5_17","volume-title":"Graph Drawing and Network Visualization","author":"M Kaufmann","year":"2018","unstructured":"Kaufmann, M., Pach, J., T\u00f3th, G., Ueckerdt, T.: The number of crossings in multigraphs with no empty lens. In: Biedl, T., Kerren, A. (eds.) GD 2018. LNCS, vol. 11282, pp. 242\u2013254. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-04414-5_17"},{"key":"16_CR4","volume-title":"Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks","author":"FT Leighton","year":"1983","unstructured":"Leighton, F.T.: Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks. MIT Press, Cambridge (1983)"},{"key":"16_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0039-7","volume-title":"Lectures on Discrete Geometry","author":"J Matousek","year":"2002","unstructured":"Matousek, J.: Lectures on Discrete Geometry. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/978-1-4613-0039-7"},{"key":"16_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/978-3-030-68766-3_28","volume-title":"Graph Drawing and Network Visualization","author":"J Pach","year":"2020","unstructured":"Pach, J., Tardos, G., T\u00f3th, G.: Crossings between non-homotopic edges. In: GD 2020. LNCS, vol. 12590, pp. 359\u2013371. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-68766-3_28"},{"issue":"4","key":"16_CR7","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1007\/s00454-018-00052-z","volume":"63","author":"J Pach","year":"2020","unstructured":"Pach, J., T\u00f3th, G.: A crossing lemma for multigraphs. Discrete Comput. Geom. 63(4), 918\u2013933 (2020). https:\/\/doi.org\/10.1007\/s00454-018-00052-z","journal-title":"Discrete Comput. Geom."},{"key":"16_CR8","doi-asserted-by":"publisher","first-page":"367","DOI":"10.7155\/jgaa.00298","volume":"17","author":"M Schaefer","year":"2013","unstructured":"Schaefer, M.: Toward a theory of planarity: Hanani-Tutte and planarity variants. J. Graph Algorithms Appl. 17, 367\u2013440 (2013)","journal-title":"J. Graph Algorithms Appl."},{"key":"16_CR9","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1017\/S0963548397002976","volume":"6","author":"LA Sz\u00e9kely","year":"1997","unstructured":"Sz\u00e9kely, L.A.: Crossing numbers and hard erd\u00f6s problems in discrete geometry. Comb. Probab. Comput. 6, 353\u2013358 (1997)","journal-title":"Comb. Probab. Comput."},{"key":"16_CR10","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/S0021-9800(70)80007-2","volume":"8","author":"WT Tutte","year":"1970","unstructured":"Tutte, W.T.: Toward a theory of crossing numbers. J. Comb. Theory Ser. A 8, 45\u201353 (1970)","journal-title":"J. Comb. Theory Ser. A"}],"container-title":["Lecture Notes in Computer Science","Graph Drawing and Network Visualization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-92931-2_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T01:01:51Z","timestamp":1766365311000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-92931-2_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030929305","9783030929312"],"references-count":10,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-92931-2_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"23 December 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Graph Drawing and Network Visualization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"T\u00fcbingen","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 September 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 September 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gd2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/algo.inf.uni-tuebingen.de\/gd2021\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"74","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"23","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.02","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"8.6","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}