{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T12:22:35Z","timestamp":1768479755628,"version":"3.49.0"},"reference-count":20,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[1986,6,1]],"date-time":"1986-06-01T00:00:00Z","timestamp":517968000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":9908,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1986,6]]},"DOI":"10.1016\/0012-365x(86)90009-9","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T23:31:50Z","timestamp":1027639910000},"page":"147-153","source":"Crossref","is-referenced-by-count":38,"special_numbering":"C","title":["On some metric and combinatorial geometric problems"],"prefix":"10.1016","volume":"60","author":[{"given":"P.","family":"Erd\u00f6s","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0012-365X(86)90009-9_BIB1_1","first-page":"99","article-title":"On some problems of elementary and combinatorial geometry","volume":"103","author":"Erd\u00f6s","year":"1975","journal-title":"Ann. Math. Ser. 4"},{"key":"10.1016\/0012-365X(86)90009-9_BIB1_2","first-page":"137","article-title":"Some applications of graph theory and combinatorial methods to number theory and geometry","volume":"25","year":"1981","journal-title":"Coll. Math. Soc. J. Bolyai"},{"key":"10.1016\/0012-365X(86)90009-9_BIB1_3","series-title":"Geom. and Diff. Geom.","first-page":"46","article-title":"Some combinatorial problems in geometry","volume":"792","year":"1980"},{"key":"10.1016\/0012-365X(86)90009-9_BIB2","doi-asserted-by":"crossref","first-page":"248","DOI":"10.2307\/2305092","article-title":"On sets of distances of n points","volume":"53","author":"Erd\u00f6s","year":"1946","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/0012-365X(86)90009-9_BIB3","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1073\/pnas.32.12.331","article-title":"On sets of integers which contain no three terms in arithmetic progression","volume":"32","author":"Behrend","year":"1946","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"10.1016\/0012-365X(86)90009-9_BIB4","doi-asserted-by":"crossref","DOI":"10.1090\/S0002-9939-1950-0035809-8","article-title":"Some remarks on set theory","volume":"1","author":"Erd\u00f6s","year":"1950","journal-title":"Proc. Amer. Math. Soc."},{"key":"10.1016\/0012-365X(86)90009-9_BIB5_1","doi-asserted-by":"crossref","first-page":"148","DOI":"10.2307\/2312883","article-title":"On a problem of P. Erd\u00f6s","volume":"70","author":"Altman","year":"1963","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/0012-365X(86)90009-9_BIB5_2","doi-asserted-by":"crossref","first-page":"329","DOI":"10.4153\/CMB-1972-060-0","article-title":"Some theorems on convex polygons","volume":"15","year":"1972","journal-title":"Canad. Math. Bull."},{"key":"10.1016\/0012-365X(86)90009-9_BIB6_1","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0097-3165(84)90047-5","article-title":"Unit distances","volume":"37","author":"Beck","year":"1984","journal-title":"J.C.T. Ser. A"},{"key":"10.1016\/0012-365X(86)90009-9_BIB6_2","first-page":"293","article-title":"Unit distances in the Euclidean Plane, Graph Theory and Combinatorics","author":"Spencer","year":"1984","journal-title":"Proc. Cambridge Comb. Conf. Acad. Press"},{"key":"10.1016\/0012-365X(86)90009-9_BIB6_3","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/BF02579194","article-title":"Extremal problems in discrete geometry","volume":"3","author":"Szemer\u00e9di","year":"1983","journal-title":"Combinatorica"},{"key":"10.1016\/0012-365X(86)90009-9_BIB6_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF02579184","article-title":"On the lattice property in the plane and some problems of Dirac, Motzkin and Erd\u00f6s in combinatorial geometry","volume":"3","author":"Beck","year":"1983","journal-title":"Combinatorica"},{"key":"10.1016\/0012-365X(86)90009-9_BIB7","first-page":"354","article-title":"The number of different distances determined by n points in the plane","volume":"36","author":"Chung","year":"1984","journal-title":"J.C.T. Ser. A."},{"key":"10.1016\/0012-365X(86)90009-9_BIB8","first-page":"451","article-title":"New Views on Some Old Questions of Combinatorial Geometry","volume":"Vol. 17","author":"Gr\u00fcbaum","year":"1976"},{"key":"10.1016\/0012-365X(86)90009-9_BIB9_1","first-page":"463","article-title":"A combinatorial problem in Geometry","volume":"2","author":"Erd\u00f6s","year":"1950","journal-title":"Compositio Math."},{"key":"10.1016\/0012-365X(86)90009-9_BIB9_2","first-page":"53","article-title":"On some extremum problems in geometry","volume":"3\u20134","author":"Erd\u00f6s","year":"1960","journal-title":"Ann. Univ. Sci. Univ. Budapest"},{"key":"10.1016\/0012-365X(86)90009-9_BIB10_1","first-page":"116","article-title":"Konvexe F\u00fcnfecke in ebenen Punktmengen","volume":"33","author":"Harborth","year":"1978","journal-title":"Elem. Math."},{"key":"10.1016\/0012-365X(86)90009-9_BIB10_2","doi-asserted-by":"crossref","first-page":"482","DOI":"10.4153\/CMB-1983-077-8","article-title":"Sets with no empty convex 7-gons","volume":"46","author":"Horton","year":"1983","journal-title":"Canad. Math. Bulletin"},{"key":"10.1016\/0012-365X(86)90009-9_BIB11","unstructured":"G. Pardy, P. Erd\u00f6s, Some Extremal Problems in Geometry IV, Proc. 7th S-E Conf. Combinatories, Graph Theory, and Computing, pp. 307\u2013322."},{"key":"10.1016\/0012-365X(86)90009-9_BIB12","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF01895954","article-title":"Linear problems in combinatorial number theory","volume":"26","author":"Koml\u00f3s","year":"1975","journal-title":"Acta Math. Acad. Sci. Hungar"}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0012365X86900099?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0012365X86900099?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T07:27:33Z","timestamp":1555140453000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0012365X86900099"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,6]]},"references-count":20,"alternative-id":["0012365X86900099"],"URL":"https:\/\/doi.org\/10.1016\/0012-365x(86)90009-9","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[1986,6]]}}}