{"id":"https://openalex.org/W1522265958","doi":"https://doi.org/10.37236/988","title":"Existentially Closed BIBD Block-Intersection Graphs","display_name":"Existentially Closed BIBD Block-Intersection Graphs","publication_year":2007,"publication_date":"2007-10-16","ids":{"openalex":"https://openalex.org/W1522265958","doi":"https://doi.org/10.37236/988","mag":"1522265958"},"language":"en","primary_location":{"id":"doi:10.37236/988","is_oa":true,"landing_page_url":"https://doi.org/10.37236/988","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r70/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r70/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056540475","display_name":"Neil A. McKay","orcid":null},"institutions":[{"id":"https://openalex.org/I130438778","display_name":"Memorial University of Newfoundland","ror":"https://ror.org/04haebc03","country_code":"CA","type":"education","lineage":["https://openalex.org/I130438778"]},{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Neil A. McKay","raw_affiliation_strings":["Department of Mathematics and Statistics Memorial University of Newfoundland St. John's, Newfoundland Canada. A1C 5S7","Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics Memorial University of Newfoundland St. John's, Newfoundland Canada. A1C 5S7","institution_ids":["https://openalex.org/I130438778"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5","institution_ids":["https://openalex.org/I129902397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087426538","display_name":"David A. Pike","orcid":"https://orcid.org/0000-0001-8952-3016"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]},{"id":"https://openalex.org/I130438778","display_name":"Memorial University of Newfoundland","ror":"https://ror.org/04haebc03","country_code":"CA","type":"education","lineage":["https://openalex.org/I130438778"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David A. Pike","raw_affiliation_strings":["Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5","Department of Mathematics and Statistics Memorial University of Newfoundland St. John's, Newfoundland Canada. A1C 5S7"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5","institution_ids":["https://openalex.org/I129902397"]},{"raw_affiliation_string":"Department of Mathematics and Statistics Memorial University of Newfoundland St. John's, Newfoundland Canada. A1C 5S7","institution_ids":["https://openalex.org/I130438778"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056540475"],"corresponding_institution_ids":["https://openalex.org/I129902397","https://openalex.org/I130438778"],"apc_list":null,"apc_paid":null,"fwci":1.7941,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84381487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9822999835014343,"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":0.9037150144577026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7925039529800415},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7306668758392334},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6328446865081787},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5212379097938538},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.49296998977661133},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48298728466033936},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.4151355028152466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3971228003501892},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.09359374642372131},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0683630108833313}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9037150144577026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7925039529800415},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7306668758392334},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6328446865081787},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5212379097938538},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.49296998977661133},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48298728466033936},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.4151355028152466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3971228003501892},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.09359374642372131},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0683630108833313},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/988","is_oa":true,"landing_page_url":"https://doi.org/10.37236/988","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r70/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:research.library.mun.ca:463","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401319","display_name":"Memorial University Research Repository (Memorial University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130438778","host_organization_name":"Memorial University of Newfoundland","host_organization_lineage":["https://openalex.org/I130438778"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/988","is_oa":true,"landing_page_url":"https://doi.org/10.37236/988","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r70/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1522265958.pdf","grobid_xml":"https://content.openalex.org/works/W1522265958.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W258588718","https://openalex.org/W1979946760","https://openalex.org/W2103458580","https://openalex.org/W2334275286","https://openalex.org/W2729869097"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W91590591","https://openalex.org/W159772521","https://openalex.org/W2950100995","https://openalex.org/W3170064006","https://openalex.org/W2281582664","https://openalex.org/W2554039769","https://openalex.org/W1893408579"],"abstract_inverted_index":{"A":[0],"graph":[1,64,69],"$G$":[2],"with":[3,19,57,116,138,192],"vertex":[4,29,40,48,71],"set":[5,59,72],"$V$":[6],"is":[7,36,44,67,181],"said":[8],"to":[9,38,46],"be":[10],"$n$-existentially":[11,110],"closed":[12],"if,":[13],"for":[14],"every":[15,22],"$S":[16],"\\subset":[17],"V$":[18],"$|S|=n$":[20],"and":[21,80,85,89,104,122,130,152,183,194],"$T":[23],"\\subseteq":[24],"S$,":[25],"there":[26],"exists":[27],"a":[28,52],"$x":[30],"\\in":[31],"V-S$":[32],"such":[33,75],"that":[34,76,125,141,158,177],"$x$":[35],"adjacent":[37,45,83],"each":[39],"of":[41,49,136,171],"$T$":[42],"but":[43],"no":[47],"$S-T$.":[50],"Given":[51],"combinatorial":[53],"design":[54],"${\\cal":[55,60,73],"D}$":[56],"block":[58,102,117],"B}$,":[61],"its":[62],"block-intersection":[63,107,128,166,198],"$G_{{\\cal":[65],"D}}$":[66],"the":[68,114,134,169],"having":[70],"B}$":[74],"two":[77],"vertices":[78],"$b_1$":[79,88],"$b_2$":[81,90],"are":[82,109,142],"if":[84,87],"only":[86,159],"have":[91,126,164,196],"non-empty":[92],"intersection.":[93],"In":[94,168],"this":[95],"paper":[96],"we":[97,156,175,184],"study":[98],"BIBDs":[99,115,137,191],"(balanced":[100],"incomplete":[101],"designs)":[103],"when":[105],"their":[106],"graphs":[108,129],"closed.":[111],"We":[112],"characterise":[113],"size":[118],"$k":[119],"\\geq":[120,146,150,154,179],"3$":[121,180],"index":[123,139],"$\\lambda=1$":[124,140],"2-e.c.":[127,197],"establish":[131],"bounds":[132],"on":[133],"parameters":[135],"$n$-e.c.":[143,165],"where":[144],"$n":[145,153,178],"3$.":[147],"For":[148],"$\\lambda":[149],"2$":[151],"2$,":[155],"prove":[157],"simple":[160],"$\\lambda$-fold":[161,172],"designs":[162],"can":[163],"graphs.":[167,199],"case":[170],"triple":[173,188],"systems":[174,189],"show":[176],"impossible,":[182],"determine":[185],"which":[186],"2-fold":[187],"(i.e.,":[190],"$k=3$":[193],"$\\lambda=2$)":[195]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
