{"doi":"10.1007/s00454-017-9883-x","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"last_name":"Balitskiy","first_name":"Alexey","full_name":"Balitskiy, Alexey"},{"first_name":"Mikhail","full_name":"Grigorev, Mikhail","last_name":"Grigorev"}],"_id":"1064","abstract":[{"lang":"eng","text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets."}],"publication":"Discrete & Computational Geometry","publication_status":"published","type":"journal_article","has_accepted_license":"1","volume":59,"date_updated":"2023-09-20T12:08:51Z","isi":1,"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"external_id":{"isi":["000432205500011"]},"page":"1001-1009","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"status":"public","file_date_updated":"2019-01-18T09:27:36Z","oa":1,"ddc":["516","000"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:49:57Z","month":"06","citation":{"ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete &#38; Computational Geometry. 59(4), 1001–1009.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00454-017-9883-x\">https://doi.org/10.1007/s00454-017-9883-x</a>.","apa":"Akopyan, A., Balitskiy, A., &#38; Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-017-9883-x\">https://doi.org/10.1007/s00454-017-9883-x</a>","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete &#38; Computational Geometry 59 (2018) 1001–1009.","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. <i>Discrete &#38; Computational Geometry</i>. 2018;59(4):1001-1009. doi:<a href=\"https://doi.org/10.1007/s00454-017-9883-x\">10.1007/s00454-017-9883-x</a>","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” <i>Discrete &#38; Computational Geometry</i>, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:<a href=\"https://doi.org/10.1007/s00454-017-9883-x\">10.1007/s00454-017-9883-x</a>.","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” <i>Discrete &#38; Computational Geometry</i>, vol. 59, no. 4. Springer, pp. 1001–1009, 2018."},"title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","quality_controlled":"1","scopus_import":"1","oa_version":"Published Version","issue":"4","publist_id":"6324","language":[{"iso":"eng"}],"intvolume":"        59","file":[{"creator":"dernst","file_id":"5844","date_updated":"2019-01-18T09:27:36Z","access_level":"open_access","file_name":"2018_DiscreteComp_Akopyan.pdf","success":1,"relation":"main_file","date_created":"2019-01-18T09:27:36Z","file_size":482518,"content_type":"application/pdf"}],"day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ec_funded":1,"publisher":"Springer","article_type":"original","year":"2018","license":"https://creativecommons.org/licenses/by/4.0/","date_published":"2018-06-01T00:00:00Z"}