{"id":"https://openalex.org/W2042077324","doi":"https://doi.org/10.1137/0402044","title":"Pair Labellings with Given Distance","display_name":"Pair Labellings with Given Distance","publication_year":1989,"publication_date":"1989-11-01","ids":{"openalex":"https://openalex.org/W2042077324","doi":"https://doi.org/10.1137/0402044","mag":"2042077324"},"language":"en","primary_location":{"id":"doi:10.1137/0402044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0402044","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://conservancy.umn.edu/bitstreams/92a1af3d-ffec-445c-9e38-a12659a90343/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023439517","display_name":"Zolt\u00e1n F\u00fcredi","orcid":"https://orcid.org/0000-0001-7335-991X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Z. Furedi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011011757","display_name":"Jerrold R. Griggs","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. R. Griggs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058820400","display_name":"Daniel J. Kleitman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. J. Kleitman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8645,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.9130932,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":"4","first_page":"491","last_page":"499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987999796867371,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987999796867371,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9983000159263611,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.888893723487854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7943857908248901},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.608614981174469},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5948047637939453},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5276347994804382},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4663013517856598}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.888893723487854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7943857908248901},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.608614981174469},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5948047637939453},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5276347994804382},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4663013517856598}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0402044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0402044","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:conservancy.umn.edu:11299/4854","is_oa":true,"landing_page_url":"http://purl.umn.edu/4854","pdf_url":"https://conservancy.umn.edu/bitstreams/92a1af3d-ffec-445c-9e38-a12659a90343/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/4854","is_oa":true,"landing_page_url":"http://purl.umn.edu/4854","pdf_url":"https://conservancy.umn.edu/bitstreams/92a1af3d-ffec-445c-9e38-a12659a90343/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2042077324.pdf"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2003995429","https://openalex.org/W2027882009","https://openalex.org/W2033563973","https://openalex.org/W2038074073","https://openalex.org/W2077575555","https://openalex.org/W2095145505","https://openalex.org/W2164679805","https://openalex.org/W4212973889"],"related_works":["https://openalex.org/W2125677183","https://openalex.org/W2038606831","https://openalex.org/W1719252778","https://openalex.org/W922283457","https://openalex.org/W3087852249","https://openalex.org/W2293240310","https://openalex.org/W2347260277","https://openalex.org/W4287018471","https://openalex.org/W2422813311","https://openalex.org/W2025517193"],"abstract_inverted_index":{"Given":[0],"a":[1,29,41],"graph":[2,85],"G":[3,25],"and":[4,93],"$d":[5,128],"\\in":[6,107],"\\mathbb{Z}^+$,":[7,108],"the":[8,17,70,80,84,109],"pair":[9,30],"labelling":[10],"number,":[11],"$r(G,d)$,":[12],"is":[13,60,124],"defined":[14],"to":[15,132],"be":[16,27],"minimum":[18],"n":[19],"such":[20,40],"that":[21,43,86,97],"each":[22],"vertex":[23],"in":[24,39],"can":[26],"assigned":[28],"of":[31,58,67,73,83,89,115],"numbers":[32,46],"from":[33],"$\\{":[34],"1,":[35],"\\cdots":[36],",n\\}":[37],"$":[38],"way":[42],"any":[44],"two":[45],"used":[47],"at":[48,53,100],"adjacent":[49],"vertices":[50,92],"differ":[51],"by":[52,62,78],"least":[54,101],"d.":[55],"A":[56,119],"question":[57],"Roberts\u2019":[59],"answered":[61],"determining":[63,79],"all":[64],"possible":[65],"values":[66],"$r(G,d)$":[68],"given":[69],"chromatic":[71,81],"number":[72,82],"G.":[74],"The":[75],"answer":[76],"follows":[77],"has":[87],"pairs":[88,96,116],"integers":[90],"as":[91],"edges":[94],"joining":[95],"are":[98,117],"distance":[99],"d":[102],"apart.":[103],"For":[104],"general":[105,122],"$t":[106],"analogous":[110],"questions":[111],"for":[112,121,127],"t-sets":[113],"instead":[114],"considered.":[118],"solution":[120],"t":[123],"conjectured":[125],"which,":[126],"=":[129],"1$,":[130],"reduces":[131],"Lov\u00e1sz's":[133],"theorem":[134],"on":[135],"Kneser":[136],"graphs.":[137]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}