{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T02:32:20Z","timestamp":1771036340421,"version":"3.50.1"},"reference-count":232,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2019,2,21]],"date-time":"2019-02-21T00:00:00Z","timestamp":1550707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"\u201cAlgoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni\u201d - Ricerca di Base 2018, Dip. Eng. Univ. of Perugia"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Comput. Surv."],"published-print":{"date-parts":[[2020,1,31]]},"abstract":"<jats:p>Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of nonplanar graphs in terms of forbidden crossing configurations. The aim of this survey is to describe the main research directions in this area, the most prominent known results, and some of the most challenging open problems.<\/jats:p>","DOI":"10.1145\/3301281","type":"journal-article","created":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T17:01:44Z","timestamp":1550854904000},"page":"1-37","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":59,"title":["A Survey on Graph Drawing Beyond Planarity"],"prefix":"10.1145","volume":"52","author":[{"given":"Walter","family":"Didimo","sequence":"first","affiliation":[{"name":"Universit\u00e0 degli Studi di Perugia, Perugia, Italy"}]},{"given":"Giuseppe","family":"Liotta","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Perugia, Perugia, Italy"}]},{"given":"Fabrizio","family":"Montecchiani","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Perugia, Perugia, Italy"}]}],"member":"320","published-online":{"date-parts":[[2019,2,21]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/3115960.3116064"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2014.05.025"},{"key":"e_1_2_1_3_1","volume-title":"On topological graphs with at most four crossings per edge. CoRR abs\/1509.01932","author":"Ackerman Eyal","year":"2015"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2014.02.003"},{"key":"e_1_2_1_5_1","volume-title":"T\u00f3th","author":"Ackerman Eyal","year":"2010"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/100819564"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00453"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2006.08.002"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1989.tb22429.x"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-03841-4_8"},{"key":"e_1_2_1_11_1","volume-title":"Kobourov","author":"Jawaherul Alam Md.","year":"2015"},{"key":"e_1_2_1_12_1","volume-title":"Proceedings of the WADS 2015 (LNCS)","volume":"9214","author":"Jawaherul Alam Md.","year":"2015"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187731"},{"key":"e_1_2_1_14_1","volume-title":"Giuseppe Di Battista, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani, and Ignaz Rutter.","author":"Angelini Patrizio","year":"2017"},{"key":"e_1_2_1_15_1","volume-title":"On RAC drawings of graphs with one bend per edge. CoRR abs\/1808.10470","author":"Angelini Patrizio","year":"2018"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.03.005"},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the GD 2017 (LNCS)","volume":"10692","author":"Angelini Patrizio","year":"2017"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00217"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2014.08.001"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-34191-5_19"},{"key":"e_1_2_1_21_1","volume-title":"Turning cliques into paths to achieve planarity. CoRR abs\/1808.08925","author":"Angelini Patrizio","year":"2018"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00250"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/800249.807437"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00282"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00274"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxs088"},{"key":"e_1_2_1_27_1","volume-title":"Orthogonal and smooth orthogonal layouts of 1-planar graphs with low edge complexity. CoRR abs\/1808.10536","author":"Argyriou Evmorfia N.","year":"2018"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2011.11.008"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-015-0002-1"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36763-2_50"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00347"},{"key":"e_1_2_1_32_1","first-page":"2","article-title":"Graphs","volume":"3","author":"Avital S.","year":"1966","journal-title":"Gilyonot Lematematika"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2017.08.015"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.05.029"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00457"},{"key":"e_1_2_1_36_1","volume-title":"Strictly convex drawings of planar graphs. CoRR abs\/cs\/0507030","author":"B\u00e1r\u00e1ny Imre","year":"2005"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.265"},{"key":"e_1_2_1_38_1","volume-title":"Proceedings of the Fourth International Conference on Entity-Relationship Approach: The Use of {ER} Concept in Knowledge Representation. IEEE Computer Society and North-Holland, 312--319","author":"Batini Carlo","year":"1985"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.5555\/10665.10670"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/2945.468391"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-016-0203-2"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-016-0200-5"},{"key":"e_1_2_1_43_1","volume-title":"Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani, and Chrysanthi N. Raftopoulou.","author":"Bekos Michael A.","year":"2018"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.05.039"},{"key":"e_1_2_1_45_1","volume-title":"A heuristic approach towards drawings of graphs with high crossing resolution. CoRR abs\/1808.10519","author":"Bekos Michael A.","year":"2018"},{"key":"e_1_2_1_46_1","volume-title":"Raftopoulou","author":"Bekos Michael A.","year":"2016"},{"key":"e_1_2_1_47_1","volume-title":"Proceedings of the SoCG 2017 (LIPIcs)","volume":"77","author":"Bekos Michael A.","year":"2017"},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00388"},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90021-2"},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0083-x"},{"key":"e_1_2_1_51_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-017-9939-y"},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00398"},{"key":"e_1_2_1_53_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2015.04.020"},{"key":"e_1_2_1_54_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2017.07.009"},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2014.01.015"},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1109\/IISA.2016.7785427"},{"key":"e_1_2_1_57_1","volume-title":"Handbook on Graph Drawing and Visualization.","author":"Bl\u00e4sius Thomas"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02941309"},{"key":"e_1_2_1_59_1","doi-asserted-by":"crossref","volume-title":"Extremal Graph Theory","author":"Bollob\u00e1s B\u00e9la","DOI":"10.1201\/b16132-57"},{"key":"e_1_2_1_60_1","doi-asserted-by":"publisher","DOI":"10.1109\/IV.2007.65"},{"key":"e_1_2_1_61_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00466"},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36763-2_29"},{"key":"e_1_2_1_63_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00330"},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00455"},{"key":"e_1_2_1_65_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2018.06.006"},{"key":"e_1_2_1_66_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-016-0226-8"},{"key":"e_1_2_1_67_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.04.026"},{"key":"e_1_2_1_68_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2006.05.006"},{"key":"e_1_2_1_69_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-55566-4_12"},{"key":"e_1_2_1_70_1","volume-title":"Research Problems in Discrete Geometry","author":"Bra\u00df Peter"},{"key":"e_1_2_1_71_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00438"},{"key":"e_1_2_1_72_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-30347-0_7"},{"key":"e_1_2_1_73_1","doi-asserted-by":"publisher","DOI":"10.1109\/IISA.2015.7387994"},{"key":"e_1_2_1_74_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00316"},{"key":"e_1_2_1_75_1","volume-title":"Handbook of Graph Drawing and Visualization","author":"Buchheim Christoph"},{"key":"e_1_2_1_76_1","doi-asserted-by":"publisher","DOI":"10.5555\/1967396.1967400"},{"key":"e_1_2_1_77_1","doi-asserted-by":"publisher","DOI":"10.1137\/120872310"},{"key":"e_1_2_1_78_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(92)90003-G"},{"key":"e_1_2_1_79_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1980.4308390"},{"key":"e_1_2_1_80_1","volume-title":"Proceedings of the GD 2017 (LNCS)","volume":"10692","author":"Chaplick Steven","year":"2017"},{"key":"e_1_2_1_81_1","volume-title":"Compact drawings of 1-planar graphs with right-angle crossings and few bends. CoRR abs\/1806.10044","author":"Chaplick Steven","year":"2018"},{"key":"e_1_2_1_82_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-014-9935-z"},{"key":"e_1_2_1_83_1","doi-asserted-by":"publisher","DOI":"10.5555\/1496770.1496812"},{"key":"e_1_2_1_84_1","volume-title":"Proceedings of the SoCG 2016 (LIPIcs)","volume":"51","author":"Chimani Markus","year":"2016"},{"key":"e_1_2_1_85_1","doi-asserted-by":"publisher","DOI":"10.1145\/1064092.1064093"},{"key":"e_1_2_1_86_1","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1702363C"},{"key":"e_1_2_1_87_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00461"},{"key":"e_1_2_1_88_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02122694"},{"key":"e_1_2_1_89_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00136"},{"key":"e_1_2_1_90_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021819591250015X"},{"key":"e_1_2_1_91_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.05.017"},{"key":"e_1_2_1_92_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-004-1106-1"},{"key":"e_1_2_1_93_1","volume-title":"A greedy heuristic for crossing-angle maximization. CoRR abs\/1807.09483","author":"Demel Almut","year":"2018"},{"key":"e_1_2_1_94_1","volume-title":"Proceedings of the GD 2001 (LNCS)","volume":"2265","author":"Battista Giuseppe Di"},{"key":"e_1_2_1_95_1","volume-title":"Tollis","author":"Battista Giuseppe Di","year":"1999"},{"key":"e_1_2_1_96_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90123-5"},{"key":"e_1_2_1_97_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187850"},{"key":"e_1_2_1_98_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-012-9706-7"},{"key":"e_1_2_1_99_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-017-0324-2"},{"key":"e_1_2_1_100_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.12.024"},{"key":"e_1_2_1_101_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxu017"},{"key":"e_1_2_1_102_1","volume-title":"Handbook on Graph Drawing and Visualization.","author":"Giacomo Emilio Di"},{"key":"e_1_2_1_103_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-010-9275-6"},{"key":"e_1_2_1_104_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxv048"},{"key":"e_1_2_1_105_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-34611-8_12"},{"key":"e_1_2_1_106_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2013.03.001"},{"key":"e_1_2_1_107_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxw075"},{"key":"e_1_2_1_108_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jvlc.2014.05.001"},{"key":"e_1_2_1_109_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195907002276"},{"key":"e_1_2_1_110_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00376"},{"key":"e_1_2_1_111_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-73915-1_37"},{"key":"e_1_2_1_112_1","volume-title":"Proceedings of the GD 2017 (LNCS)","volume":"10692","author":"Giacomo Emilio Di","year":"2018"},{"key":"e_1_2_1_113_1","doi-asserted-by":"publisher","DOI":"10.1145\/568522.568523"},{"key":"e_1_2_1_114_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00099"},{"key":"e_1_2_1_115_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2013.01.013"},{"key":"e_1_2_1_116_1","volume-title":"Encyclopedia of Algorithms. 2308--2312.","author":"Didimo Walter"},{"key":"e_1_2_1_117_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2010.05.023"},{"key":"e_1_2_1_118_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.05.025"},{"key":"e_1_2_1_119_1","volume-title":"Thirty Essays on Geometric Graph Theory","author":"Didimo Walter"},{"key":"e_1_2_1_120_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00224"},{"key":"e_1_2_1_121_1","doi-asserted-by":"publisher","DOI":"10.5555\/1964371.1964387"},{"key":"e_1_2_1_122_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.09.048"},{"key":"e_1_2_1_123_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.11.017"},{"key":"e_1_2_1_124_1","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.2002.0582"},{"key":"e_1_2_1_125_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2014.07.005"},{"key":"e_1_2_1_126_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1062879"},{"key":"e_1_2_1_127_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00454"},{"key":"e_1_2_1_128_1","volume-title":"Notes on large angle crossing graphs. Chicago J. Theor. Comput. Sci. 2011","author":"Dujmovic Vida","year":"2011"},{"key":"e_1_2_1_129_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2017.05.006"},{"key":"e_1_2_1_130_1","first-page":"339","article-title":"On linear layouts of graphs. Discr. Math. 8","volume":"6","author":"Dujmovic Vida","year":"2004","journal-title":"Theor. Comp. Sci."},{"key":"e_1_2_1_131_1","first-page":"155","article-title":"Stacks, queues and tracks: Layouts of graph subdivisions. Discr. Math. 8","volume":"7","author":"Dujmovic Vida","year":"2005","journal-title":"Theor. Comp. Sci."},{"key":"e_1_2_1_132_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-21840-3_25"},{"key":"e_1_2_1_133_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2012.11.019"},{"key":"e_1_2_1_134_1","volume-title":"Proceedings of the ACSC","author":"Eades P.","year":"1986"},{"key":"e_1_2_1_135_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01187020"},{"key":"e_1_2_1_136_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004530010020"},{"key":"e_1_2_1_137_1","doi-asserted-by":"publisher","DOI":"10.5555\/2794579.3118807"},{"key":"e_1_2_1_138_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2008.05.005"},{"key":"e_1_2_1_139_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00343"},{"key":"e_1_2_1_140_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.06.045"},{"key":"e_1_2_1_141_1","first-page":"229","article-title":"On straight-line representation of planar graphs. Acta Sci","volume":"11","author":"F\u00e1ry Istv\u00e1n","year":"1948","journal-title":"Math."},{"key":"e_1_2_1_142_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-28076-4_19"},{"key":"e_1_2_1_143_1","doi-asserted-by":"publisher","DOI":"10.1137\/110858586"},{"key":"e_1_2_1_144_1","doi-asserted-by":"publisher","DOI":"10.1137\/0604033"},{"key":"e_1_2_1_145_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794277123"},{"key":"e_1_2_1_146_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2014.05.001"},{"key":"e_1_2_1_147_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-007-0010-x"},{"key":"e_1_2_1_148_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00456"},{"key":"e_1_2_1_149_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1991.185452"},{"key":"e_1_2_1_150_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-004-1128-8"},{"key":"e_1_2_1_151_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70582"},{"key":"e_1_2_1_152_1","volume-title":"Proceedings of the MFCS 2017 (LIPIcs)","volume":"83","author":"Hoffmann Michael","year":"2017"},{"key":"e_1_2_1_153_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.147"},{"key":"e_1_2_1_154_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01450.x"},{"key":"e_1_2_1_155_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-014-9890-8"},{"key":"e_1_2_1_156_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-50106-2_25"},{"key":"e_1_2_1_157_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53174-7_29"},{"key":"e_1_2_1_158_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32241-9_29"},{"key":"e_1_2_1_159_1","doi-asserted-by":"publisher","DOI":"10.1145\/321850.321852"},{"key":"e_1_2_1_160_1","doi-asserted-by":"publisher","DOI":"10.1109\/APVIS.2007.329282"},{"key":"e_1_2_1_161_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00779-011-0473-2"},{"key":"e_1_2_1_162_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jvlc.2014.03.001"},{"key":"e_1_2_1_163_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jvlc.2011.12.002"},{"key":"e_1_2_1_164_1","doi-asserted-by":"publisher","DOI":"10.1109\/PACIFICVIS.2008.4475457"},{"key":"e_1_2_1_165_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2000.1727"},{"key":"e_1_2_1_166_1","doi-asserted-by":"crossref","unstructured":"Michael J\u00fcnger and Petra Mutzel (Eds.). 2004. Graph Drawing Software. Springer.  Michael J\u00fcnger and Petra Mutzel (Eds.). 2004. Graph Drawing Software. Springer.","DOI":"10.1007\/978-3-642-18638-7"},{"key":"e_1_2_1_167_1","volume-title":"Graphs Combin. (LNCS)","author":"Kainen Paul C."},{"key":"e_1_2_1_168_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-014-1690-9"},{"key":"e_1_2_1_169_1","volume-title":"The density of fan-planar graphs. CoRR abs\/1403.6184","author":"Kaufmann Michael","year":"2014"},{"key":"e_1_2_1_170_1","doi-asserted-by":"crossref","unstructured":"Michael Kaufmann and Dorothea Wagner (Eds.). 2001. Drawing Graphs. Springer.  Michael Kaufmann and Dorothea Wagner (Eds.). 2001. Drawing Graphs. Springer.","DOI":"10.1007\/3-540-44969-8"},{"key":"e_1_2_1_171_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00046"},{"key":"e_1_2_1_172_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2009.45"},{"key":"e_1_2_1_173_1","doi-asserted-by":"publisher","DOI":"10.1145\/1250790.1250848"},{"key":"e_1_2_1_174_1","volume-title":"Drawing subcubic 1-planar graphs with few bends, few slopes, and large angles. CoRR abs\/1808.08496","author":"Kindermann Philipp","year":"2018"},{"key":"e_1_2_1_175_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2017.06.002"},{"key":"e_1_2_1_176_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21630"},{"key":"e_1_2_1_177_1","unstructured":"Yaakov S. Kupitz. 1979. Extremal Problems in Combinatorial Geometry. Matematisk institut Aarhus Universitet.  Yaakov S. Kupitz. 1979. Extremal Problems in Combinatorial Geometry. Matematisk institut Aarhus Universitet."},{"key":"e_1_2_1_178_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1980.13"},{"key":"e_1_2_1_179_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.12.004"},{"key":"e_1_2_1_180_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(80)90060-4"},{"key":"e_1_2_1_181_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2015.11.011"},{"key":"e_1_2_1_182_1","volume-title":"Ortho-polygon visibility representations of 3-connected 1-plane graphs. CoRR abs\/1807.01247","author":"Liotta Giuseppe","year":"2018"},{"key":"e_1_2_1_183_1","volume-title":"Proceedings of the 10th Southeastern Conference on Combinatorics, Graph Theory, and Computing. 727--738","author":"Liu P. C."},{"key":"e_1_2_1_184_1","volume-title":"Searching for and classifying the finite set of minor-minimal non-apex graphs. Master\u2019s thesis","author":"Mike Pierce"},{"key":"e_1_2_1_185_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623498334013"},{"key":"e_1_2_1_186_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00199-1"},{"key":"e_1_2_1_187_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2011.09.008"},{"key":"e_1_2_1_188_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18469-7_40"},{"key":"e_1_2_1_189_1","first-page":"21","article-title":"Permutation procedure for minimising the number of crossings in a network","volume":"115","author":"Nicholson T. A. J.","year":"1968","journal-title":"Proc. IEE"},{"key":"e_1_2_1_190_1","volume-title":"Proceedings, 4th S.E. Conference on Combinatorics, Graph Theory, and Computing, Frederick Hoffman, Roy B. Levow, and Robert S. D. Thomas (Eds.). Utilitas Mathematics Publ. Inc., 459","author":"Ollmann Taylor L.","year":"1974"},{"key":"e_1_2_1_191_1","volume-title":"Handbook of Discr. and Comp. Geom","author":"Pach J\u00e1nos"},{"key":"e_1_2_1_192_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-005-0616-1"},{"key":"e_1_2_1_193_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2003.09.019"},{"key":"e_1_2_1_194_1","doi-asserted-by":"publisher","DOI":"10.5555\/3116646.3116831"},{"key":"e_1_2_1_195_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02086610"},{"key":"e_1_2_1_196_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574361"},{"key":"e_1_2_1_197_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01215922"},{"key":"e_1_2_1_198_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00007258"},{"key":"e_1_2_1_199_1","doi-asserted-by":"publisher","DOI":"10.1145\/777792.777807"},{"key":"e_1_2_1_200_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0953-5438(00)00032-1"},{"key":"e_1_2_1_201_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016344215610"},{"key":"e_1_2_1_202_1","volume-title":"Ein Sechsfarbenproblem auf der Kugel. Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg 29, 1--2","author":"Ringel Gerhard","year":"1965"},{"key":"e_1_2_1_203_1","unstructured":"Maxwell J. Roberts. 2012. Underground Maps Unravelled: Explorations in Information Design. Maxwell J Roberts.  Maxwell J. Roberts. 2012. Underground Maps Unravelled: Explorations in Information Design. Maxwell J Roberts."},{"key":"e_1_2_1_204_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.08.001"},{"key":"e_1_2_1_205_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01202354"},{"key":"e_1_2_1_206_1","doi-asserted-by":"publisher","DOI":"10.37236\/2713"},{"key":"e_1_2_1_207_1","volume-title":"Proceedings of the ACM-SIAM SoDA","author":"Schnyder Walter","year":"1990"},{"key":"e_1_2_1_208_1","volume-title":"Proceedings of the CCCG 1996","author":"Shermer Thomas C.","year":"1996"},{"key":"e_1_2_1_209_1","volume-title":"Tollis","author":"Six Janet M.","year":"2013"},{"key":"e_1_2_1_210_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1951-0041425-5"},{"key":"e_1_2_1_211_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1981.4308636"},{"key":"e_1_2_1_212_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2015.06.001"},{"key":"e_1_2_1_213_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.07.016"},{"key":"e_1_2_1_214_1","doi-asserted-by":"publisher","DOI":"10.1137\/0216030"},{"key":"e_1_2_1_215_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187705"},{"key":"e_1_2_1_216_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120306"},{"key":"e_1_2_1_217_1","unstructured":"C. D. Toth J. O\u2019Rourke and J. E. Goodman. 2017. Handbook of Discrete and Computional Geometry Third Edition. CRC Press.  C. D. Toth J. O\u2019Rourke and J. E. Goodman. 2017. Handbook of Discrete and Computional Geometry Third Edition. CRC Press."},{"key":"e_1_2_1_218_1","unstructured":"Klaus Truemper. 1992. Matroid Decomposition. Academic Press.  Klaus Truemper. 1992. Matroid Decomposition. Academic Press."},{"key":"e_1_2_1_219_1","doi-asserted-by":"publisher","DOI":"10.5555\/1963635.1963641"},{"key":"e_1_2_1_220_1","doi-asserted-by":"publisher","DOI":"10.5555\/647549.728926"},{"key":"e_1_2_1_221_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009364"},{"key":"e_1_2_1_222_1","volume-title":"Proceedings of the GD 2010 (LNCS)","volume":"6502","author":"van Kreveld Marc J.","year":"2010"},{"key":"e_1_2_1_223_1","unstructured":"Massimo Vignelli. 2008. New York Subway Map http:\/\/secondavenuesagas.com\/2008\/05\/02\/mens-vogue-calls-on-vignelli-for-a-long-awaited-update\/.  Massimo Vignelli. 2008. New York Subway Map http:\/\/secondavenuesagas.com\/2008\/05\/02\/mens-vogue-calls-on-vignelli-for-a-long-awaited-update\/."},{"key":"e_1_2_1_224_1","first-page":"26","article-title":"Bemerkungen zum vierfarbenproblem","volume":"46","author":"Wagner Klaus","year":"1936","journal-title":"Jahresbericht der Deutschen Mathematiker-Vereinigung"},{"key":"e_1_2_1_225_1","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.ivs.9500013"},{"key":"e_1_2_1_226_1","doi-asserted-by":"publisher","DOI":"10.5555\/857191.857733"},{"key":"e_1_2_1_227_1","doi-asserted-by":"publisher","DOI":"10.1145\/323233.323253"},{"key":"e_1_2_1_228_1","unstructured":"Stephen K. Wismath. 1989. Bar-representable visibility graphs and a related network flow problem. https:\/\/open.library.ubc.ca\/cIRcle\/collections\/ubctheses\/831\/items\/1.0051983.  Stephen K. Wismath. 1989. Bar-representable visibility graphs and a related network flow problem. https:\/\/open.library.ubc.ca\/cIRcle\/collections\/ubctheses\/831\/items\/1.0051983."},{"key":"e_1_2_1_229_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2004.06.001"},{"key":"e_1_2_1_230_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(89)90032-9"},{"key":"e_1_2_1_231_1","doi-asserted-by":"publisher","DOI":"10.2478\/s11533-012-0094-7"},{"key":"e_1_2_1_232_1","doi-asserted-by":"publisher","DOI":"10.1109\/TST.2013.6509098"}],"container-title":["ACM Computing Surveys"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3301281","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3301281","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:58:02Z","timestamp":1750208282000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3301281"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,21]]},"references-count":232,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1,31]]}},"alternative-id":["10.1145\/3301281"],"URL":"https:\/\/doi.org\/10.1145\/3301281","relation":{},"ISSN":["0360-0300","1557-7341"],"issn-type":[{"value":"0360-0300","type":"print"},{"value":"1557-7341","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,21]]},"assertion":[{"value":"2018-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-10-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-02-21","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}