{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:21:18Z","timestamp":1750306878536,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":42,"publisher":"ACM","license":[{"start":{"date-parts":[[2013,6,17]],"date-time":"2013-06-17T00:00:00Z","timestamp":1371427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2013,6,17]]},"DOI":"10.1145\/2462356.2462370","type":"proceedings-article","created":{"date-parts":[[2014,1,7]],"date-time":"2014-01-07T17:18:46Z","timestamp":1389115126000},"page":"27-36","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["The graphs of planar soap bubbles"],"prefix":"10.1145","author":[{"given":"David","family":"Eppstein","sequence":"first","affiliation":[{"name":"University of California, Irvine, Irvine, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,6,17]]},"reference":[{"key":"e_1_3_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1052796.1052804"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/0216006"},{"key":"e_1_3_2_1_3_1","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/3-540-44634-6_3","volume-title":"7th Worksh. Algorithms and Data Structures","author":"Bern M.","year":"2001","unstructured":"M. Bern and D. Eppstein . Optimal M\u00f6bius transformations for information visualization and meshing . In 7th Worksh. Algorithms and Data Structures , volume 2125 of LNCS , pages 14 -- 25 . Springer , 2001 . M. Bern and D. Eppstein. Optimal M\u00f6bius transformations for information visualization and meshing. In 7th Worksh. Algorithms and Data Structures, volume 2125 of LNCS, pages 14--25. Springer, 2001."},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0189-84"},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/237218.237401"},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(02)00099-8"},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2012.0392"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/90397.92364"},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25878-7_30"},{"key":"e_1_3_2_1_10_1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/978-3-642-18469-7_17","volume-title":"Proc. 18th Int. Symp. Graph Drawing","author":"Duncan C. A.","year":"2011","unstructured":"C. A. Duncan , D. Eppstein , M. T. Goodrich , S. G. Kobourov , and M. N\u00f6llenburg . Drawing trees with perfect angular resolution and polynomial area . In U. Brandes and S. Cornelsen, editors, Proc. 18th Int. Symp. Graph Drawing , volume 6502 of Lecture Notes in Computer Science , pages 183 -- 194 . Springer-Verlag , 2011 . C. A. Duncan, D. Eppstein, M. T. Goodrich, S. G. Kobourov, and M. N\u00f6llenburg. Drawing trees with perfect angular resolution and polynomial area. In U. Brandes and S. Cornelsen, editors, Proc. 18th Int. Symp. Graph Drawing, volume 6502 of Lecture Notes in Computer Science, pages 183--194. Springer-Verlag, 2011."},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00251"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1119\/1.3247982"},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36763-2_12"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1810959.1811030"},{"key":"e_1_3_2_1_15_1","volume-title":"Instabilities in two-dimensional flower and chain clusters of bubbles. Coll. Surf. A, 309(1--3):64--70","author":"Fortes M. A.","year":"2007","unstructured":"M. A. Fortes , M. F. Vaz , S. J. Cox , and P. I. C. Teixeira . Instabilities in two-dimensional flower and chain clusters of bubbles. Coll. Surf. A, 309(1--3):64--70 , 2007 . M. A. Fortes, M. F. Vaz, S. J. Cox, and P. I. C. Teixeira. Instabilities in two-dimensional flower and chain clusters of bubbles. Coll. Surf. A, 309(1--3):64--70, 2007."},{"issue":"4","key":"e_1_3_2_1_16_1","first-page":"440","article-title":"Cannonballs and honeycombs","volume":"47","author":"Hales T. C.","year":"2000","unstructured":"T. C. Hales . Cannonballs and honeycombs . Notices Amer. Math. Soc. , 47 ( 4 ): 440 -- 449 , 2000 . T. C. Hales. Cannonballs and honeycombs. Notices Amer. Math. Soc., 47(4):440--449, 2000.","journal-title":"Notices Amer. Math. Soc."},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004540010071"},{"key":"e_1_3_2_1_18_1","volume-title":"Double bubbles minimize. Annals of Mathematics (2nd Ser.), 151(2):459--515","author":"Hass J.","year":"2000","unstructured":"J. Hass and R. Schlafly . Double bubbles minimize. Annals of Mathematics (2nd Ser.), 151(2):459--515 , 2000 . J. Hass and R. Schlafly. Double bubbles minimize. Annals of Mathematics (2nd Ser.), 151(2):459--515, 2000."},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1991.0103"},{"issue":"5","key":"e_1_3_2_1_20_1","doi-asserted-by":"crossref","first-page":"377","DOI":"10.5951\/MT.72.5.0377","article-title":"Smart soap bubbles can do calculus","volume":"72","author":"Hoffman D. T.","year":"1979","unstructured":"D. T. Hoffman . Smart soap bubbles can do calculus . The Mathematics Teacher , 72 ( 5 ): 377 -- 385 , 1979 . D. T. Hoffman. Smart soap bubbles can do calculus. The Mathematics Teacher, 72(5):377--385, 1979.","journal-title":"The Mathematics Teacher"},{"key":"e_1_3_2_1_21_1","volume-title":"Proof of the double bubble conjecture. Annals of Mathematics (2nd Ser.), 155(2):459--489","author":"Hutchings M.","year":"2002","unstructured":"M. Hutchings , F. Morgan , M. Ritor\u00e9 , and A. Ros . Proof of the double bubble conjecture. Annals of Mathematics (2nd Ser.), 155(2):459--489 , 2002 . M. Hutchings, F. Morgan, M. Ritor\u00e9, and A. Ros. Proof of the double bubble conjecture. Annals of Mathematics (2nd Ser.), 155(2):459--489, 2002."},{"issue":"5","key":"e_1_3_2_1_22_1","first-page":"514","article-title":"The soap film: an analogue computer","volume":"64","author":"Isenberg C.","year":"1976","unstructured":"C. Isenberg . The soap film: an analogue computer . American Scientist , 64 ( 5 ): 514 -- 518 , 1976 . C. Isenberg. The soap film: an analogue computer. American Scientist, 64(5):514--518, 1976.","journal-title":"American Scientist"},{"key":"e_1_3_2_1_23_1","volume-title":"The Science of Soap Films and Soap Bubbles","author":"Isenberg C.","year":"1978","unstructured":"C. Isenberg . Chapter 5. The Laplace--Young Equation . In The Science of Soap Films and Soap Bubbles . Dover , 1978 . C. Isenberg. Chapter 5. The Laplace--Young Equation. In The Science of Soap Films and Soap Bubbles. Dover, 1978."},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.5555\/800033.800872"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.5555\/800033.800874"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-37-00336-3"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90340-Y"},{"key":"e_1_3_2_1_28_1","volume-title":"Geometric Measure Theory: A Beginner's Guide","author":"Morgan F.","year":"2009","unstructured":"F. Morgan . Geometric Measure Theory: A Beginner's Guide . Academic Press , 4 th edition, 2009 . F. Morgan. Geometric Measure Theory: A Beginner's Guide. Academic Press, 4th edition, 2009.","edition":"4"},{"key":"e_1_3_2_1_29_1","volume-title":"Gauthier-Villiard","author":"Plateau J. A. F.","year":"1873","unstructured":"J. A. F. Plateau . Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires . Gauthier-Villiard , Paris , 1873 . J. A. F. Plateau. Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires. Gauthier-Villiard, Paris, 1873."},{"key":"e_1_3_2_1_30_1","volume-title":"39th Southeast Conf. ACM","author":"Pootheri S. K.","year":"2001","unstructured":"S. K. Pootheri . Decomposition characterizations of classes of 2-connected graphs . In 39th Southeast Conf. ACM , 2001 . S. K. Pootheri. Decomposition characterizations of classes of 2-connected graphs. In 39th Southeast Conf. ACM, 2001."},{"issue":"2","key":"e_1_3_2_1_31_1","article-title":"Least-perimeter partitions of the sphere","volume":"8","author":"Quinn C.","year":"2007","unstructured":"C. Quinn . Least-perimeter partitions of the sphere . Rose--Hulman Inst. Tech. Undergrad. Math. J. , 8 ( 2 ), 2007 . Appendix by Quinn Maurmann. C. Quinn. Least-perimeter partitions of the sphere. Rose--Hulman Inst. Tech. Undergrad. Math. J., 8(2), 2007. Appendix by Quinn Maurmann.","journal-title":"Rose--Hulman Inst. Tech. Undergrad. Math. J."},{"key":"e_1_3_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9301-0"},{"key":"e_1_3_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00216"},{"key":"e_1_3_2_1_34_1","first-page":"1","volume-title":"Encyclopadie der mathematischen Wissenschaften, Band 3 (Geometries)","author":"Steinitz E.","year":"1922","unstructured":"E. Steinitz . Polyeder und Raumeinteilungen . In Encyclopadie der mathematischen Wissenschaften, Band 3 (Geometries) , pages 1 -- 139 . 1922 . E. Steinitz. Polyeder und Raumeinteilungen. In Encyclopadie der mathematischen Wissenschaften, Band 3 (Geometries), pages 1--139. 1922."},{"key":"e_1_3_2_1_35_1","volume-title":"The Theory of Discrete Analytic Functions","author":"Stephenson K.","year":"2005","unstructured":"K. Stephenson . Introduction to Circle Packing : The Theory of Discrete Analytic Functions . Cambridge University Press , 2005 . K. Stephenson. Introduction to Circle Packing: The Theory of Discrete Analytic Functions. Cambridge University Press, 2005."},{"key":"e_1_3_2_1_36_1","series-title":"NATO Adv","first-page":"379","volume-title":"J.-F","author":"Sullivan J. M.","year":"1997","unstructured":"J. M. Sullivan . The geometry of bubbles and foams . In J.-F . Sadoc and N. Rivier, editors, Foams and Emulsions: Proc . NATO Advanced Study Inst. on Foams and Emulsions, Emulsions and Cellular Materials, Carg\u00e8se, Corsica, 12--24 May , 1997 , volume 354 of NATO Adv . Sci. Inst. Ser. E Appl. Sci., pages 379 -- 402 , Dordrecht, 1999. Kluwer Acad . Publ. J. M. Sullivan. The geometry of bubbles and foams. In J.-F. Sadoc and N. Rivier, editors, Foams and Emulsions: Proc. NATO Advanced Study Inst. on Foams and Emulsions, Emulsions and Cellular Materials, Carg\u00e8se, Corsica, 12--24 May, 1997, volume 354 of NATO Adv. Sci. Inst. Ser. E Appl. Sci., pages 379--402, Dordrecht, 1999. Kluwer Acad. Publ."},{"key":"e_1_3_2_1_37_1","volume-title":"The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Annals of Mathematics (2nd Ser.), 103(3):489--539","author":"Taylor J. E.","year":"1976","unstructured":"J. E. Taylor . The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Annals of Mathematics (2nd Ser.), 103(3):489--539 , 1976 . J. E. Taylor. The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Annals of Mathematics (2nd Ser.), 103(3):489--539, 1976."},{"issue":"151","key":"e_1_3_2_1_38_1","first-page":"503","article-title":"On the division of space with minimum partitional area","volume":"24","author":"Thompson W.","year":"1887","unstructured":"W. Thompson . On the division of space with minimum partitional area . Philosophical Magazine , 24 ( 151 ): 503 , 1887 . W. Thompson. On the division of space with minimum partitional area. Philosophical Magazine, 24(151):503, 1887.","journal-title":"Philosophical Magazine"},{"key":"e_1_3_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-28.3.336"},{"key":"e_1_3_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1140\/epje\/i200101168"},{"key":"e_1_3_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1080\/09500839408241577"},{"key":"e_1_3_2_1_42_1","unstructured":"W. Wichiramala. The Planar Triple Bubble Problem. PhD thesis Univ. of Illinois at Urbana-Champaign 2002.  W. Wichiramala. The Planar Triple Bubble Problem. PhD thesis Univ. of Illinois at Urbana-Champaign 2002."}],"event":{"name":"SoCG '13: Symposium on Computational Geometry 2013","sponsor":["SIGGRAPH ACM Special Interest Group on Computer Graphics and Interactive Techniques","SIGACT ACM Special Interest Group on Algorithms and Computation Theory"],"location":"Rio de Janeiro Brazil","acronym":"SoCG '13"},"container-title":["Proceedings of the twenty-ninth annual symposium on Computational geometry"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2462356.2462370","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2462356.2462370","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:18:29Z","timestamp":1750234709000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2462356.2462370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,17]]},"references-count":42,"alternative-id":["10.1145\/2462356.2462370","10.1145\/2462356"],"URL":"https:\/\/doi.org\/10.1145\/2462356.2462370","relation":{},"subject":[],"published":{"date-parts":[[2013,6,17]]},"assertion":[{"value":"2013-06-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}