{"id":"https://openalex.org/W2028300942","doi":"https://doi.org/10.1002/(sici)1097-0118(199711)26:3<147::aid-jgt5>3.0.co;2-r","title":"On the structure of extremal graphs of high girth","display_name":"On the structure of extremal graphs of high girth","publication_year":1997,"publication_date":"1997-11-01","ids":{"openalex":"https://openalex.org/W2028300942","doi":"https://doi.org/10.1002/(sici)1097-0118(199711)26:3<147::aid-jgt5>3.0.co;2-r","mag":"2028300942"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199711)26:3<147::aid-jgt5>3.0.co;2-r","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199711)26:3<147::aid-jgt5>3.0.co;2-r","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031529103","display_name":"Felix Lazebnik","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Felix Lazebnik","raw_affiliation_strings":["Department of Mathematical Sciences, University of Delaware, Newark, DE 19716"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Delaware, Newark, DE 19716","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100338623","display_name":"Ping Wang","orcid":"https://orcid.org/0000-0002-0379-9183"},"institutions":[{"id":"https://openalex.org/I197191942","display_name":"St. Francis Xavier University","ror":"https://ror.org/01wcaxs37","country_code":"CA","type":"education","lineage":["https://openalex.org/I197191942"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ping Wang","raw_affiliation_strings":["Department of Mathematics, Computing and Information Systems, St. Francis Xavier University, Antigonish, Nova Scotia, Canada,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Computing and Information Systems, St. Francis Xavier University, Antigonish, Nova Scotia, Canada,","institution_ids":["https://openalex.org/I197191942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031529103"],"corresponding_institution_ids":["https://openalex.org/I86501945"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.16222962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"3","first_page":"147","last_page":"153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987000226974487,"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/T11476","display_name":"Graph theory and applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8858959674835205},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8715521693229675},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.592731773853302},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.5879888534545898},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5189526081085205},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"Extremal graph theory","score":0.49757054448127747},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4758146405220032},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41326141357421875},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4104343056678772},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19961223006248474},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.12805554270744324}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8858959674835205},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8715521693229675},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.592731773853302},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.5879888534545898},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5189526081085205},{"id":"https://openalex.org/C12595997","wikidata":"https://www.wikidata.org/wiki/Q739245","display_name":"Extremal graph theory","level":5,"score":0.49757054448127747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4758146405220032},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41326141357421875},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4104343056678772},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19961223006248474},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.12805554270744324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199711)26:3<147::aid-jgt5>3.0.co;2-r","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199711)26:3<147::aid-jgt5>3.0.co;2-r","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W174566906","https://openalex.org/W1510730180","https://openalex.org/W1569752386","https://openalex.org/W1966969478","https://openalex.org/W2012280556","https://openalex.org/W2076597612","https://openalex.org/W2082538734","https://openalex.org/W2087806988","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2311783135","https://openalex.org/W2903806635","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W3101625811","https://openalex.org/W2165950148","https://openalex.org/W4300101996"],"abstract_inverted_index":{"Let":[0],"n":[1,25,43,79,97,102],"\u2265":[2,76,92,103,125],"3":[3,99],"be":[4,11],"a":[5,12,95],"positive":[6],"integer,":[7],"and":[8,28,56,78],"let":[9],"G":[10,40],"simple":[13],"graph":[14],"of":[15,21,34,53],"order":[16],"v":[17,75,85,91,120],"containing":[18],"no":[19],"cycles":[20],"length":[22],"smaller":[23],"than":[24],"+":[26,44,123],"1":[27],"having":[29],"the":[30,71,106,112,115],"greatest":[31],"possible":[32],"number":[33],"edges":[35],"(an":[36],"extremal":[37,54],"graph).":[38],"Does":[39],"contain":[41],"an":[42],"1-cycle?":[45],"In":[46],"this":[47,61,68],"paper":[48],"we":[49,109],"establish":[50],"some":[51],"properties":[52],"graphs":[55],"present":[57],"several":[58],"results":[59],"where":[60,94],"question":[62,116],"is":[63,69,86,117],"answered":[64],"affirmatively.":[65],"For":[66],"example,":[67],"always":[70],"case":[72],"for":[73,119],"(i)":[74],"8":[77],"=":[80,96,121],"5,":[81],"or":[82],"(ii)":[83],"when":[84],"large":[87],"compared":[88],"to":[89,114],"n:":[90],",":[93,101],"-":[98,100],"12.":[104],"On":[105],"other":[107],"hand":[108],"prove":[110],"that":[111],"answer":[113],"negative":[118],"2n":[122],"2":[124],"26.":[126],"\u00a9":[127],"1997":[128,139],"John":[129],"Wiley":[130],"&":[131],"Sons,":[132],"Inc.":[133],"J":[134],"Graph":[135],"Theory":[136],"26:":[137],"147\u2013153,":[138]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
