{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:51:12Z","timestamp":1774626672616,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":12,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540895497","type":"print"},{"value":"9783540895503","type":"electronic"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"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":[[2008]]},"DOI":"10.1007\/978-3-540-89550-3_10","type":"book-chapter","created":{"date-parts":[[2008,11,18]],"date-time":"2008-11-18T09:02:28Z","timestamp":1226998948000},"page":"90-100","source":"Crossref","is-referenced-by-count":7,"title":["A Minimal Planar Point Set with Specified Disjoint Empty Convex Subsets"],"prefix":"10.1007","author":[{"given":"Kiyoshi","family":"Hosono","sequence":"first","affiliation":[]},{"given":"Masatsugu","family":"Urabe","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"10_CR1","unstructured":"Aichholzer, O., Huemer, C., Renkl, S., Speckmann, B., T\u00f3th, C.D.: On Pseudo-Convex Decompositions, Partitions and Coverings. In: 21\n                  th\n                 European Workshop on Computational Geometry, Eindhoven, The Netherlands, pp. 89\u201392 (2005)"},{"key":"10_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/3-540-47738-1_7","volume-title":"Discrete and Computational Geometry","author":"I. B\u00e1r\u00e1ny","year":"2001","unstructured":"B\u00e1r\u00e1ny, I., K\u00e1rolyi, G.: Problems and results around the Erd\u0151s-Szekeres convex polygon theorem. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 2000. LNCS, vol.\u00a02098, pp. 91\u2013105. Springer, Heidelberg (2001)"},{"key":"10_CR3","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/BF02414146","volume":"103","author":"P. Erd\u0151s","year":"1975","unstructured":"Erd\u0151s, P.: On some problems of elementary and combinatorial geometry. Ann. Mat. Pura. Appl.\u00a0103, 99\u2013108 (1975)","journal-title":"Ann. Mat. Pura. Appl."},{"key":"10_CR4","first-page":"463","volume":"2","author":"P. Erd\u0151s","year":"1935","unstructured":"Erd\u0151s, P., Szekeres, G.: A combinatorial problem in geometry. Compositio Mathematica\u00a02, 463\u2013470 (1935)","journal-title":"Compositio Mathematica"},{"key":"10_CR5","unstructured":"Gerken, T.: Empty convex hexagons in planar point sets. Discrete Comput. Geom. (to appear)"},{"key":"10_CR6","first-page":"116","volume":"33","author":"H. Harborth","year":"1978","unstructured":"Harborth, H.: Konvexe F\u00fcnfecke in ebenen Punktmengen. Elem. Math.\u00a033, 116\u2013118 (1978)","journal-title":"Elem. Math."},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"482","DOI":"10.4153\/CMB-1983-077-8","volume":"26","author":"J.D. Horton","year":"1983","unstructured":"Horton, J.D.: Sets with no empty 7-gons. Canadian Math. Bull.\u00a026, 482\u2013484 (1983)","journal-title":"Canadian Math. Bull."},{"key":"10_CR8","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/S0925-7721(01)00023-2","volume":"20","author":"K. Hosono","year":"2001","unstructured":"Hosono, K., Urabe, M.: On the number of disjoint convex quadrilaterals for a plannar point set. Comp. Geom. Theory Appl.\u00a020, 97\u2013104 (2001)","journal-title":"Comp. Geom. Theory Appl."},{"key":"10_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/11589440_12","volume-title":"Discrete and Computational Geometry","author":"K. Hosono","year":"2005","unstructured":"Hosono, K., Urabe, M.: On the minimum size of a point set containing two non-intersecting empty convex polygons. In: Akiyama, J., Kano, M., Tan, X. (eds.) JCDCG 2004. LNCS, vol.\u00a03742, pp. 117\u2013122. Springer, Heidelberg (2005)"},{"key":"10_CR10","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s00454-002-2829-x","volume":"29","author":"M.H. Overmars","year":"2003","unstructured":"Overmars, M.H.: Finding sets of points without empty convex 6-gons. Discrete Comput. Geom.\u00a029, 153\u2013158 (2003)","journal-title":"Discrete Comput. Geom."},{"key":"10_CR11","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1007\/PL00009363","volume":"19","author":"G. T\u00f3th","year":"1998","unstructured":"T\u00f3th, G., Valtr, P.: Note on the Erd\u0151s-Szekeres theorem. Discrete Comput. Geom.\u00a019, 457\u2013459 (1998)","journal-title":"Discrete Comput. Geom."},{"key":"10_CR12","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0166-218X(94)00120-3","volume":"64","author":"M. Urabe","year":"1996","unstructured":"Urabe, M.: On a partition into convex polygons. Discrete Appl. Math.\u00a064, 179\u2013191 (1996)","journal-title":"Discrete Appl. Math."}],"container-title":["Lecture Notes in Computer Science","Computational Geometry and Graph Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-89550-3_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T21:02:50Z","timestamp":1551646970000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-89550-3_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9783540895497","9783540895503"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-89550-3_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008]]}}}