{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,16]],"date-time":"2025-03-16T04:16:56Z","timestamp":1742098616522,"version":"3.38.0"},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642258770"},{"type":"electronic","value":"9783642258787"}],"license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-25878-7_4","type":"book-chapter","created":{"date-parts":[[2011,12,15]],"date-time":"2011-12-15T02:23:04Z","timestamp":1323915784000},"page":"26-38","source":"Crossref","is-referenced-by-count":6,"title":["Proportional Contact Representations of Planar Graphs"],"prefix":"10.1007","author":[{"given":"Muhammad Jawaherul","family":"Alam","sequence":"first","affiliation":[]},{"given":"Therese","family":"Biedl","sequence":"additional","affiliation":[]},{"given":"Stefan","family":"Felsner","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Kaufmann","sequence":"additional","affiliation":[]},{"given":"Stephen G.","family":"Kobourov","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"4_CR1","doi-asserted-by":"crossref","unstructured":"Alam, M.J., Biedl, T., Felsner, S., Gerasch, A., Kaufmann, M., Kobourov, S.G., Ueckert, T.: Computing cartograms with optimal complexity (submitted, 2011)","DOI":"10.1145\/2261250.2261254"},{"key":"4_CR2","doi-asserted-by":"crossref","unstructured":"Alam, M.J., Biedl, T., Felsner, S., Kaufmann, M., Kobourov, S.G.: Proportional contact representations of planar graphs. Technical Report CS-2011-11. University of Waterloo (2011)","DOI":"10.1007\/978-3-642-25878-7_4"},{"key":"4_CR3","unstructured":"Badent, M., Binucci, C., Giacomo, E.D., Didimo, W., Felsner, S., Giordano, F., Kratochv\u00edl, J., Palladino, P., Patrignani, M., Trotta, F.: Homothetic triangle contact representations of planar graphs. In: CCCG 2007, pp. 233\u2013236 (2007)"},{"key":"4_CR4","doi-asserted-by":"crossref","unstructured":"Buchsbaum, A.L., Gansner, E.R., Procopiuc, C.M., Venkatasubramanian, S.: Rectangular layouts and contact graphs. ACM Transactions on Algorithms\u00a04(1) (2008)","DOI":"10.1145\/1328911.1328919"},{"key":"4_CR5","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1017\/S0963548300001139","volume":"3","author":"H. Fraysseix de","year":"1994","unstructured":"de Fraysseix, H., de Mendez, P.O., Rosenstiehl, P.: On triangle contact graphs. Combinatorics, Probability and Computing\u00a03, 233\u2013246 (1994)","journal-title":"Combinatorics, Probability and Computing"},{"issue":"1","key":"4_CR6","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\u00a010(1), 41\u201351 (1990)","journal-title":"Combinatorica"},{"key":"4_CR7","unstructured":"Debrunner, H.: Aufgabe 260. Elemente der Mathematik\u00a012 (1957)"},{"key":"4_CR8","doi-asserted-by":"crossref","unstructured":"Felsner, S., Francis, M.C.: Contact representations of planar graphs with cubes. In: Proc. ACM Symposium on Computational Geometry (2011)","DOI":"10.1145\/1998196.1998250"},{"key":"4_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/978-3-642-12200-2_37","volume-title":"LATIN 2010: Theoretical Informatics","author":"E.R. Gansner","year":"2010","unstructured":"Gansner, E.R., Hu, Y.F., Kaufmann, M., Kobourov, S.G.: Optimal Polygonal Representation of Planar Graphs. In: L\u00f3pez-Ortiz, A. (ed.) LATIN 2010. LNCS, vol.\u00a06034, pp. 417\u2013432. Springer, Heidelberg (2010)"},{"key":"4_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1007\/978-3-642-18469-7_23","volume-title":"Graph Drawing","author":"E.R. Gansner","year":"2011","unstructured":"Gansner, E.R., Hu, Y., Kobourov, S.G.: On Touching Triangle Graphs. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol.\u00a06502, pp. 250\u2013261. Springer, Heidelberg (2011)"},{"key":"4_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1007\/978-3-642-18469-7_24","volume-title":"Graph Drawing","author":"D. Gon\u00e7alves","year":"2011","unstructured":"Gon\u00e7alves, D., L\u00e9v\u00eaque, B., Pinlou, A.: Triangle Contact Representations and Duality. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol.\u00a06502, pp. 262\u2013273. Springer, Heidelberg (2011)"},{"key":"4_CR12","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/0012-365X(91)90069-E","volume":"97","author":"I. Hartman","year":"1991","unstructured":"Hartman, I., Newman, I., Ziv, R.: On grid intersection graphs. Discrete Mathematics\u00a097, 41\u201352 (1991)","journal-title":"Discrete Mathematics"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"Heilmann, R., Keim, D.A., Panse, C., Sips, M.: Recmap: Rectangular map approximations. In: 10th IEEE Symp.\u00a0on Information Visualization (InfoVis 2004), pp. 33\u201340 (2004)","DOI":"10.1109\/INFVIS.2004.57"},{"key":"4_CR14","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/S0012-365X(00)00263-6","volume":"235","author":"P. Hlin\u011bn\u00fd","year":"2001","unstructured":"Hlin\u011bn\u00fd, P.: Contact graphs of line segments are NP-complete. Discr. Math.\u00a0235, 95\u2013106 (2001)","journal-title":"Discr. Math."},{"key":"4_CR15","first-page":"141","volume":"88","author":"P. Koebe","year":"1936","unstructured":"Koebe, P.: Kontaktprobleme der konformen Abbildung. Berichte \u00fcber die Verhandlungen der S\u00e4chsischen Akademie der Wissenschaften zu Leipzig. Math.-Phys. Kl.\u00a088, 141\u2013164 (1936)","journal-title":"Berichte \u00fcber die Verhandlungen der S\u00e4chsischen Akademie der Wissenschaften zu Leipzig. Math.-Phys. Kl."},{"key":"4_CR16","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1002\/net.3230150202","volume":"15","author":"K. Ko\u017ami\u0144ski","year":"1985","unstructured":"Ko\u017ami\u0144ski, K., Kinnen, E.: Rectangular duals of planar graphs. Networks\u00a015, 145\u2013157 (1985)","journal-title":"Networks"},{"issue":"8","key":"4_CR17","doi-asserted-by":"publisher","first-page":"1425","DOI":"10.1016\/j.disc.2007.07.104","volume":"308","author":"A. Lee","year":"2008","unstructured":"Lee, A., Streinu, I.: Pebble game algorithms and sparse graphs. Discrete Mathematics\u00a0308(8), 1425\u20131437 (2008)","journal-title":"Discrete Mathematics"},{"key":"4_CR18","unstructured":"Schnyder, W.: Embedding planar graphs on the grid. In: SODA, pp. 138\u2013148 (1990)"},{"key":"4_CR19","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1112\/jlms\/s1-28.3.336","volume":"28","author":"P. Ungar","year":"1953","unstructured":"Ungar, P.: On diagrams representing graphs. J. London Math. Soc.\u00a028, 336\u2013342 (1953)","journal-title":"J. London Math. Soc."},{"issue":"3","key":"4_CR20","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.comgeo.2006.06.002","volume":"37","author":"M.J. Kreveld van","year":"2007","unstructured":"van Kreveld, M.J., Speckmann, B.: On rectangular cartograms. Computational Geometry\u00a037(3), 175\u2013187 (2007)","journal-title":"Computational Geometry"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1137\/0222035","volume":"22","author":"K.-H. Yeap","year":"1993","unstructured":"Yeap, K.-H., Sarrafzadeh, M.: Floor-planning by graph dualization: 2-concave rectilinear modules. SIAM Journal on Computing\u00a022, 500\u2013526 (1993)","journal-title":"SIAM Journal on Computing"}],"container-title":["Lecture Notes in Computer Science","Graph Drawing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-25878-7_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T21:26:41Z","timestamp":1742074001000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-25878-7_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642258770","9783642258787"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-25878-7_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}