{"id":"https://openalex.org/W1992578441","doi":"https://doi.org/10.1145/1998196.1998249","title":"Sphere and dot product representations of graphs","display_name":"Sphere and dot product representations of graphs","publication_year":2011,"publication_date":"2011-06-13","ids":{"openalex":"https://openalex.org/W1992578441","doi":"https://doi.org/10.1145/1998196.1998249","mag":"1992578441"},"language":"en","primary_location":{"id":"doi:10.1145/1998196.1998249","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1998196.1998249","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1998196.1998249","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/1998196.1998249","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019911064","display_name":"Ross J. Kang","orcid":"https://orcid.org/0000-0002-4219-593X"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ross J. Kang","raw_affiliation_strings":["Durham University, Durham, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Durham University, Durham, United Kingdom","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077475001","display_name":"Tobias M\u00fcller","orcid":"https://orcid.org/0000-0002-5964-7867"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Tobias M\u00fcller","raw_affiliation_strings":["Centrum Wiskunde &amp; Informatica, Amsterdam, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde &amp; Informatica, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2873,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.46647718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"308","last_page":"314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7374919056892395},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.665859043598175},{"id":"https://openalex.org/keywords/dot-product","display_name":"Dot product","score":0.6644488573074341},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6011226177215576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5624504089355469},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.515905499458313},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.44118836522102356},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.4128410518169403},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36159345507621765},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2532787024974823},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.2522696256637573},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1015574038028717}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7374919056892395},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.665859043598175},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.6644488573074341},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6011226177215576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5624504089355469},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.515905499458313},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.44118836522102356},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.4128410518169403},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36159345507621765},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2532787024974823},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.2522696256637573},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1015574038028717}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1998196.1998249","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1998196.1998249","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1998196.1998249","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:cwi:oai:cwi.nl:18583","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/18583","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencepaper"},{"id":"pmh:cwi:oai:cwi.nl:19592","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/19592","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 47(3), 548 - 568","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1145/1998196.1998249","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1998196.1998249","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1998196.1998249","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G283985778","display_name":null,"funder_award_id":"EP/G066604/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W94985437","https://openalex.org/W176071698","https://openalex.org/W639947448","https://openalex.org/W1495794766","https://openalex.org/W1570340896","https://openalex.org/W1574151794","https://openalex.org/W1963547452","https://openalex.org/W1968034334","https://openalex.org/W1971048994","https://openalex.org/W1982378203","https://openalex.org/W2001505356","https://openalex.org/W2006753964","https://openalex.org/W2019029270","https://openalex.org/W2021111619","https://openalex.org/W2060963839","https://openalex.org/W2073694981","https://openalex.org/W2082387287","https://openalex.org/W2092468781","https://openalex.org/W2131662609","https://openalex.org/W2151549243","https://openalex.org/W2498084162","https://openalex.org/W2971330320","https://openalex.org/W4253785454","https://openalex.org/W4254205555","https://openalex.org/W4256581173","https://openalex.org/W4301808069","https://openalex.org/W6607175506","https://openalex.org/W6992347331","https://openalex.org/W6996888795"],"related_works":["https://openalex.org/W2369655046","https://openalex.org/W2019467317","https://openalex.org/W1585519779","https://openalex.org/W1965515989","https://openalex.org/W2088737283","https://openalex.org/W1999587863","https://openalex.org/W1929902734","https://openalex.org/W3104474499","https://openalex.org/W4299565411","https://openalex.org/W2131251246"],"abstract_inverted_index":{"A":[0,34],"graph":[1,6,35,41,74,89,100],"G":[2,36,92],"is":[3,30,37,65,93],"a":[4,38,88,94,97,112,124],"k-sphere":[5,95],"if":[7,20,23,42,54,57],"there":[8,43],"are":[9,44,101],"k-dimensional":[10,45],"real":[11,46],"vectors":[12,47],"v1,...,":[13],"vn":[14],"such":[15,49],"that":[16,50,82],"ij":[17,51],"\u2208":[18,52],"E(G)":[19,53],"and":[21,28,55,63,116,130],"only":[22,56],"the":[24,58,83,107,120],"distance":[25],"between":[26],"vi":[27,62],"vj":[29,64],"at":[31,66],"most":[32],"1.":[33,68],"k-dot":[39,98],"product":[40,60,99],"v1,...,vn":[48],"dot":[59],"of":[61,85,114,126],"least":[67],"By":[69],"relating":[70],"these":[71],"two":[72],"geometric":[73],"constructions":[75],"to":[76],"oriented":[77],"k-hyperplane":[78],"arrangements,":[79],"we":[80],"prove":[81],"problems":[84],"deciding,":[86],"given":[87],"G,":[90],"whether":[91],"or":[96],"NP-hard":[102],"for":[103],"all":[104],"k>1.":[105],"In":[106,119],"former":[108],"case,":[109],"this":[110,122],"proves":[111],"conjecture":[113],"Breu":[115],"Kirkpatrick":[117],"(1998).":[118,132],"latter,":[121],"answers":[123],"question":[125],"Fiduccia,":[127],"Scheinerman,":[128],"Trenk":[129],"Zito":[131]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
