{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T05:24:10Z","timestamp":1725600250338},"publisher-location":"Berlin, Heidelberg","reference-count":27,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642222993"},{"type":"electronic","value":"9783642223006"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"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":[[2011]]},"DOI":"10.1007\/978-3-642-22300-6_44","type":"book-chapter","created":{"date-parts":[[2011,8,9]],"date-time":"2011-08-09T12:41:31Z","timestamp":1312893691000},"page":"524-535","source":"Crossref","is-referenced-by-count":4,"title":["Counting Plane Graphs: Flippability and Its Applications"],"prefix":"10.1007","author":[{"given":"Michael","family":"Hoffmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Micha","family":"Sharir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adam","family":"Sheffer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Csaba D.","family":"T\u00f3th","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emo","family":"Welzl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"1","key":"44_CR1","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s00373-007-0704-5","volume":"23","author":"O. Aichholzer","year":"2007","unstructured":"Aichholzer, O., Hackl, T., Huemer, Hurtado, F., Krasser, H., Vogtenhuber, B.: On the number of plane geometric graphs. Graph. Comb.\u00a023(1), 67\u201384 (2007)","journal-title":"Graph. Comb."},{"key":"44_CR2","first-page":"9","volume":"12","author":"M. Ajtai","year":"1982","unstructured":"Ajtai, M., Chv\u00e1tal, V., Newborn, M.M., Szemer\u00e9di, E.: Crossing-free subgraphs. Annals Discrete Math.\u00a012, 9\u201312 (1982)","journal-title":"Annals Discrete Math."},{"issue":"1","key":"44_CR3","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.comgeo.2008.04.001","volume":"42","author":"P. Bose","year":"2009","unstructured":"Bose, P., Hurtado, F.: Flips in planar graphs. Comput. Geom. Theory Appl.\u00a042(1), 60\u201380 (2009)","journal-title":"Comput. Geom. Theory Appl."},{"key":"44_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/978-3-540-73545-8_12","volume-title":"Computing and Combinatorics","author":"K. Buchin","year":"2007","unstructured":"Buchin, K., Knauer, C., Kriegel, K., Schulz, A., Seidel, R.: On the number of cycles in planar graphs. In: Lin, G. (ed.) COCOON 2007. LNCS, vol.\u00a04598, pp. 97\u2013107. Springer, Heidelberg (2007)"},{"key":"44_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1007\/978-3-642-15775-2_10","volume-title":"Algorithms \u2013 ESA 2010","author":"K. Buchin","year":"2010","unstructured":"Buchin, K., Schulz, A.: On the number of spanning trees a planar graph can have. In: de Berg, M., Meyer, U. (eds.) ESA 2010. LNCS, vol.\u00a06346, pp. 110\u2013121. Springer, Heidelberg (2010)"},{"key":"44_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12971-1","volume-title":"Triangulations: Structures for Algorithms and Applications","author":"J.A. Loera De","year":"2010","unstructured":"De Loera, J.A., Rambau, J., Santos, F.: Triangulations: Structures for Algorithms and Applications. Springer, Berlin (2010)"},{"key":"44_CR7","unstructured":"Denny, M.O., Sohler, C.A.: Encoding a triangulation as a permutation of its point set. In: Proc. 9th Canadian Conf. on Computational Geometry, pp. 39\u201343 (1997)"},{"key":"44_CR8","unstructured":"Dumitrescu, A., Schulz, A., Sheffer, A., T\u00f3th, C.D.: Bounds on the maximum multiplicity of some common geometric graphs. In: Proc. 28th International Symposium on Theoretical Aspects of Computer Science, pp. 637\u2013648 (2011)"},{"key":"44_CR9","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1142\/9789814355858_0006","volume-title":"Euclidean Geometry and Computers","author":"S. Fortune","year":"1992","unstructured":"Fortune, S.: Voronoi diagrams and Delaunay triangulations. In: Du, D.A., Hwang, F.K. (eds.) Euclidean Geometry and Computers, pp. 193\u2013233. World Scientific Publishing Co., New York (1992)"},{"issue":"2","key":"44_CR10","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1142\/S0218195903001098","volume":"13","author":"J. Galtier","year":"2003","unstructured":"Galtier, J., Hurtado, F., Noy, M., P\u00e9rennes, S., Urrutia, J.: Simultaneous edge flipping in triangulations. Internat. J. Comput. Geom. Appl.\u00a013(2), 113\u2013133 (2003)","journal-title":"Internat. J. Comput. Geom. Appl."},{"key":"44_CR11","unstructured":"Garc\u00eda-Lopez, J., Nicol\u00e1s, M.: Planar point sets with large minimum convex partitions. In: Proc. 22nd Euro. Workshop Comput. Geom., Delphi, pp. 51\u201354 (2006)"},{"issue":"4","key":"44_CR12","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/S0925-7721(00)00010-9","volume":"16","author":"A. Garc\u00eda","year":"2000","unstructured":"Garc\u00eda, A., Noy, M., Tejel, J.: Lower bounds on the number of crossing-free subgraphs of K N . Comput. Geom. Theory Appl.\u00a016(4), 211\u2013221 (2000)","journal-title":"Comput. Geom. Theory Appl."},{"key":"44_CR13","volume-title":"Triangulations and Applications","author":"\u00d8. Hjelle","year":"2009","unstructured":"Hjelle, \u00d8., D\u00e6hlen, M.: Triangulations and Applications. Springer, Berlin (2009)"},{"key":"44_CR14","unstructured":"Hoffmann, M., Sharir, M., Sheffer, A., T\u00f3th, C.D., Welzl, E.: Counting Plane Graphs: Flippability and its Applications, arXiv:1012.0591"},{"key":"44_CR15","doi-asserted-by":"publisher","first-page":"1714","DOI":"10.1016\/j.disc.2008.02.008","volume":"309","author":"K. Hosono","year":"2009","unstructured":"Hosono, K.: On convex decompositions of a planar point set. Discrete Math.\u00a0309, 1714\u20131717 (2009)","journal-title":"Discrete Math."},{"key":"44_CR16","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/PL00009464","volume":"22","author":"F. Hurtado","year":"1999","unstructured":"Hurtado, F., Noy, M., Urrutia, J.: Flipping edges in triangulations. Discrete Comput. Geom.\u00a022, 333\u2013346 (1999)","journal-title":"Discrete Comput. Geom."},{"key":"44_CR17","volume-title":"Matching theory","author":"L. Lov\u00e1sz","year":"1986","unstructured":"Lov\u00e1sz, L., Plummer, M.: Matching theory. North Holland, Amsterdam (1986)"},{"key":"44_CR18","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.endm.2008.06.039","volume":"31","author":"A. Razen","year":"2008","unstructured":"Razen, A., Snoeyink, J., Welzl, E.: Number of crossing-free geometric graphs vs. triangulations. Electronic Notes in Discrete Math.\u00a031, 195\u2013200 (2008)","journal-title":"Electronic Notes in Discrete Math."},{"key":"44_CR19","unstructured":"Rib\u00f3, A.: Realizations and Counting Problems for Planar Structures: Trees and Linkages, Polytopes and Polyominos, Ph.D. thesis. Freie Universit\u00e4t Berlin (2005)"},{"key":"44_CR20","first-page":"969","volume":"2","author":"G. Rote","year":"2005","unstructured":"Rote, G.: The number of spanning trees in a planar graph. Oberwolfach Reports\u00a02, 969\u2013973 (2005)","journal-title":"Oberwolfach Reports"},{"issue":"1","key":"44_CR21","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/S0097-3165(03)00002-5","volume":"102","author":"F. Santos","year":"2003","unstructured":"Santos, F., Seidel, R.: A better upper bound on the number of triangulations of a planar point set. J. Combinat. Theory Ser. A\u00a0102(1), 186\u2013193 (2003)","journal-title":"J. Combinat. Theory Ser. A"},{"key":"44_CR22","doi-asserted-by":"crossref","unstructured":"Sharir, M., Sheffer, A.: Counting triangulations of planar point sets. Electr. J. Comb.\u00a018(1) (2011), arXiv:0911.3352v2","DOI":"10.37236\/557"},{"key":"44_CR23","doi-asserted-by":"crossref","unstructured":"Sharir, M., Welzl, E.: Random triangulations of planar point sets. In: Proc. 17th Ann. ACM-SIAM Symp. on Discrete Algorithms, pp. 860\u2013869 (2006)","DOI":"10.1145\/1137856.1137898"},{"key":"44_CR24","unstructured":"Souvaine, D.L., T\u00f3th, C.D., Winslow, A.: Simultaneously flippable edges in triangulations. In: Proc. XIV Spanish Meeting on Comput. Geom. (to appear, 2011)"},{"key":"44_CR25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511609589","volume-title":"Enumerative Combinatorics","author":"R.P. Stanley","year":"1999","unstructured":"Stanley, R.P.: Enumerative Combinatorics, vol.\u00a02. Cambridge University Press, Cambridge (1999)"},{"key":"44_CR26","volume-title":"Proc. 10th Canadian Conference on Computational Geometry","author":"J. Urrutia","year":"1998","unstructured":"Urrutia, J.: Open problem session. In: Proc. 10th Canadian Conference on Computational Geometry. McGill University, Montr\u00e9al (1998)"},{"key":"44_CR27","first-page":"26","volume":"46","author":"K. Wagner","year":"1936","unstructured":"Wagner, K.: Bemerkungen zum Vierfarbenproblem. J. Deutsch. Math.-Verein.\u00a046, 26\u201332 (1936)","journal-title":"J. Deutsch. Math.-Verein."}],"container-title":["Lecture Notes in Computer Science","Algorithms and Data Structures"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-22300-6_44","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T04:37:43Z","timestamp":1592800663000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-22300-6_44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642222993","9783642223006"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-22300-6_44","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}