{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:50:30Z","timestamp":1742914230544,"version":"3.40.3"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319272603"},{"type":"electronic","value":"9783319272610"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-27261-0_25","type":"book-chapter","created":{"date-parts":[[2015,11,26]],"date-time":"2015-11-26T01:24:59Z","timestamp":1448501099000},"page":"295-308","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Recognizing and Drawing IC-Planar Graphs"],"prefix":"10.1007","author":[{"given":"Franz J.","family":"Brandenburg","sequence":"first","affiliation":[]},{"given":"Walter","family":"Didimo","sequence":"additional","affiliation":[]},{"given":"William S.","family":"Evans","sequence":"additional","affiliation":[]},{"given":"Philipp","family":"Kindermann","sequence":"additional","affiliation":[]},{"given":"Giuseppe","family":"Liotta","sequence":"additional","affiliation":[]},{"given":"Fabrizio","family":"Montecchiani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,27]]},"reference":[{"issue":"3","key":"25_CR1","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s00454-009-9143-9","volume":"41","author":"E Ackerman","year":"2009","unstructured":"Ackerman, E.: On the maximum number of edges in topological graphs with no four pairwise crossing edges. Discrete Comput. Geom. 41(3), 365\u2013375 (2009)","journal-title":"Discrete Comput. Geom."},{"key":"25_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/978-3-319-03841-4_8","volume-title":"Graph Drawing","author":"MJ Alam","year":"2013","unstructured":"Alam, M.J., Brandenburg, F.J., Kobourov, S.G.: Straight-line grid drawings of 3-connected 1-planar graphs. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 83\u201394. Springer, Heidelberg (2013)"},{"issue":"2","key":"25_CR3","doi-asserted-by":"publisher","first-page":"569","DOI":"10.7155\/jgaa.00274","volume":"16","author":"EN Argyriou","year":"2012","unstructured":"Argyriou, E.N., Bekos, M.A., Symvonis, A.: The straight-line RAC drawing problem is NP-hard. J. Graph Algorithms Appl. 16(2), 569\u2013597 (2012)","journal-title":"J. Graph Algorithms Appl."},{"key":"25_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/978-3-319-03841-4_10","volume-title":"Graph Drawing","author":"C Auer","year":"2013","unstructured":"Auer, C., Bachmaier, C., Brandenburg, F.J., Glei\u00dfner, A., Hanauer, K., Neuwirth, D., Reislhuber, J.: Recognizing outer 1-planar graphs in linear time. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 107\u2013118. Springer, Heidelberg (2013)"},{"issue":"1","key":"25_CR5","doi-asserted-by":"publisher","first-page":"67","DOI":"10.7155\/jgaa.00347","volume":"19","author":"C Auer","year":"2015","unstructured":"Auer, C., Brandenburg, F.J., Gleiner, A., Reislhuber, J.: 1-planarity of graphs with a rotation system. J. Graph Algorithms Appl. 19(1), 67\u201386 (2015)","journal-title":"J. Graph Algorithms Appl."},{"key":"25_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1007\/978-3-662-45803-7_17","volume-title":"Graph Drawing","author":"MA Bekos","year":"2014","unstructured":"Bekos, M.A., Cornelsen, S., Grilli, L., Hong, S.-H., Kaufmann, M.: On the recognition of fan-planar and maximal outer-fan-planar graphs. In: Duncan, C., Symvonis, A. (eds.) GD 2014. LNCS, vol. 8871, pp. 198\u2013209. Springer, Heidelberg (2014)"},{"key":"25_CR7","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.tcs.2015.04.020","volume":"589","author":"C Binucci","year":"2015","unstructured":"Binucci, C., Di Giacomo, E., Didimo, W., Montecchiani, F., Patrignani, M., Symvonis, A., Tollis, I.G.: Fan-planarity: properties and complexity. Theor. Comput. Sci. 589, 76\u201385 (2015)","journal-title":"Theor. Comput. Sci."},{"key":"25_CR8","first-page":"12","volume":"41","author":"OV Borodin","year":"1984","unstructured":"Borodin, O.V.: Solution of the Ringel problem on vertex-face coloring of planar graphs and coloring of \n                      \n                        \n                      \n                      $$1$$\n                    -planar graphs. Metody Diskret Analiz. 41, 12\u201326 (1984)","journal-title":"Metody Diskret Analiz."},{"key":"25_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/978-3-642-36763-2_29","volume-title":"Graph Drawing","author":"FJ Brandenburg","year":"2013","unstructured":"Brandenburg, F.J., Eppstein, D., Glei\u00dfner, A., Goodrich, M.T., Hanauer, K., Reislhuber, J.: On the density of maximal 1-planar graphs. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 327\u2013338. Springer, Heidelberg (2013)"},{"key":"25_CR10","unstructured":"Brandenburg, F.J., Didimo, W., Evans, W.S., Kindermann, P., Liotta, G., Montecchiani, F.: Recognizing and drawing IC-planar graphs. Arxiv report (2015). Available at \n                      http:\/\/arxiv.org\/abs\/1509.00388"},{"key":"25_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/978-3-642-45030-3_16","volume-title":"Algorithms and Computation","author":"O Cheong","year":"2013","unstructured":"Cheong, O., Har-Peled, S., Kim, H., Kim, H.-S.: On the number of edges of fan-crossing free graphs. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) Algorithms and Computation. LNCS, vol. 8283, pp. 163\u2013173. Springer, Heidelberg (2013)"},{"issue":"4","key":"25_CR12","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/0020-0190(95)00020-D","volume":"54","author":"M Chrobak","year":"1995","unstructured":"Chrobak, M., Payne, T.H.: A linear-time algorithm for drawing a planar graph on a grid. Inf. Process. Lett. 54(4), 241\u2013246 (1995)","journal-title":"Inf. Process. Lett."},{"issue":"1","key":"25_CR13","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/BF02122694","volume":"10","author":"H Fraysseix de","year":"1990","unstructured":"de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41\u201351 (1990)","journal-title":"Combinatorica"},{"issue":"4","key":"25_CR14","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1007\/s00453-012-9706-7","volume":"68","author":"E Giacomo Di","year":"2014","unstructured":"Di Giacomo, E., Didimo, W., Eades, P., Liotta, G.: 2-layer right angle crossing drawings. Algorithmica 68(4), 954\u2013997 (2014)","journal-title":"Algorithmica"},{"key":"25_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/978-3-642-34611-8_12","volume-title":"Graph-Theoretic Concepts in Computer Science","author":"E Giacomo Di","year":"2012","unstructured":"Di Giacomo, E., Didimo, W., Liotta, G., Montecchiani, F.: h-Quasi planar drawings of bounded treewidth graphs in linear area. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. LNCS, vol. 7551, pp. 91\u2013102. Springer, Heidelberg (2012)"},{"issue":"8","key":"25_CR16","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1016\/j.comgeo.2013.03.001","volume":"46","author":"E Giacomo Di","year":"2013","unstructured":"Di Giacomo, E., Didimo, W., Liotta, G., Montecchiani, F.: Area requirement of graph drawings with few crossings per edge. Comput. Geom. 46(8), 909\u2013916 (2013)","journal-title":"Comput. Geom."},{"issue":"39","key":"25_CR17","doi-asserted-by":"publisher","first-page":"5156","DOI":"10.1016\/j.tcs.2011.05.025","volume":"412","author":"W Didimo","year":"2011","unstructured":"Didimo, W., Eades, P., Liotta, G.: Drawing graphs with right angle crossings. Theoretical Comput. Sci. 412(39), 5156\u20135166 (2011)","journal-title":"Theoretical Comput. Sci."},{"key":"25_CR18","first-page":"167","volume-title":"Thirty Essays on Geometric Graph Theory","author":"W Didimo","year":"2012","unstructured":"Didimo, W., Liotta, G.: The crossing angle resolution in graph drawing. In: Pach, J. (ed.) Thirty Essays on Geometric Graph Theory, pp. 167\u2013184. Springer, New York (2012)"},{"issue":"7\u20138","key":"25_CR19","doi-asserted-by":"publisher","first-page":"961","DOI":"10.1016\/j.dam.2012.11.019","volume":"161","author":"P Eades","year":"2013","unstructured":"Eades, P., Liotta, G.: Right angle crossing graphs and 1-planarity. Discrete Appl. Math. 161(7\u20138), 961\u2013969 (2013)","journal-title":"Discrete Appl. Math."},{"issue":"1","key":"25_CR20","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1137\/110858586","volume":"27","author":"J Fox","year":"2013","unstructured":"Fox, J., Pach, J., Suk, A.: The number of edges in \n                      \n                        \n                      \n                      $$k$$\n                    -quasi-planar graphs. SIAM J. Discrete Math. 27(1), 550\u2013561 (2013)","journal-title":"SIAM J. Discrete Math."},{"issue":"3","key":"25_CR21","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1137\/0604033","volume":"4","author":"MR Garey","year":"1983","unstructured":"Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM J. Algebraic Discrete Methods 4(3), 312\u2013316 (1983)","journal-title":"SIAM J. Algebraic Discrete Methods"},{"key":"25_CR22","first-page":"1","volume":"46","author":"S Hong","year":"2014","unstructured":"Hong, S., Eades, P., Katoh, N., Liotta, G., Schweitzer, P., Suzuki, Y.: A linear-time algorithm for testing outer-1-planarity. Algorithmica 46, 1\u201322 (2014)","journal-title":"Algorithmica"},{"key":"25_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/978-3-642-32241-9_29","volume-title":"Computing and Combinatorics","author":"S-H Hong","year":"2012","unstructured":"Hong, S.-H., Eades, P., Liotta, G., Poon, S.-H.: F\u00e1ry\u2019s theorem for 1-planar graphs. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds.) COCOON 2012. LNCS, vol. 7434, pp. 335\u2013346. Springer, Heidelberg (2012)"},{"key":"25_CR24","unstructured":"Kaufmann, M., Ueckerdt, T.: The density of fan-planar graphs. Arxiv report, (2014). Available at \n                      http:\/\/arxiv.org\/abs\/1403.6184"},{"issue":"1","key":"25_CR25","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1002\/jgt.21630","volume":"72","author":"VP Korzhik","year":"2013","unstructured":"Korzhik, V.P., Mohar, B.: Minimal obstructions for 1-immersions and hardness of 1-planarity testing. J. Graph Theor. 72(1), 30\u201371 (2013)","journal-title":"J. Graph Theor."},{"issue":"3","key":"25_CR26","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1002\/jgt.20448","volume":"64","author":"D Kr\u00e1l","year":"2010","unstructured":"Kr\u00e1l, D., Stacho, L.: Coloring plane graphs with independent crossings. J. Graph Theor. 64(3), 184\u2013205 (2010)","journal-title":"J. Graph Theor."},{"key":"25_CR27","unstructured":"Liotta, G.: Graph drawing beyond planarity: some results and open problems. In: Theoretical Computer Science (ICTCS 2014), pp. 3\u20138 (2014)"},{"issue":"3","key":"25_CR28","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/BF01215922","volume":"17","author":"J Pach","year":"1997","unstructured":"Pach, J., T\u00f3th, G.: Graphs drawn with few crossings per edge. Combinatorica 17(3), 427\u2013439 (1997)","journal-title":"Combinatorica"},{"issue":"3","key":"25_CR29","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1002\/jgt.3190120306","volume":"12","author":"C Thomassen","year":"1988","unstructured":"Thomassen, C.: Rectilinear drawings of graphs. J. Graph Theor. 12(3), 335\u2013341 (1988)","journal-title":"J. Graph Theor."},{"issue":"12","key":"25_CR30","doi-asserted-by":"publisher","first-page":"2045","DOI":"10.1007\/s10114-014-3763-6","volume":"30","author":"X Zhang","year":"2014","unstructured":"Zhang, X.: Drawing complete multipartite graphs on the plane with restrictions on crossings. Acta Math. Sinica 30(12), 2045\u20132053 (2014)","journal-title":"Acta Math. Sinica"},{"issue":"2","key":"25_CR31","first-page":"308","volume":"11","author":"X Zhang","year":"2013","unstructured":"Zhang, X., Liu, G.: The structure of plane graphs with independent crossings and its applications to coloring problems. Central Eur. J. Math. 11(2), 308\u2013321 (2013)","journal-title":"Central Eur. J. Math."}],"container-title":["Lecture Notes in Computer Science","Graph Drawing and Network Visualization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-27261-0_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T20:12:13Z","timestamp":1569269533000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-27261-0_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319272603","9783319272610"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-27261-0_25","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"27 November 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}