{"id":"https://openalex.org/W2150450974","doi":"https://doi.org/10.1002/jgt.3190150302","title":"The threshold weight of a graph","display_name":"The threshold weight of a graph","publication_year":1991,"publication_date":"1991-07-01","ids":{"openalex":"https://openalex.org/W2150450974","doi":"https://doi.org/10.1002/jgt.3190150302","mag":"2150450974"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190150302","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190150302","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/A5100342208","display_name":"Chi Wang","orcid":"https://orcid.org/0000-0002-2033-0870"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chi Wang","raw_affiliation_strings":["Rutcor-Rutgers Center For Or Rutgers University, New Brunswick, New Jersey"],"affiliations":[{"raw_affiliation_string":"Rutcor-Rutgers Center For Or Rutgers University, New Brunswick, New Jersey","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072551968","display_name":"Adrian Williams","orcid":"https://orcid.org/0000-0003-2098-808X"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. C. Williams","raw_affiliation_strings":["Rutcor-Rutgers Center For Or Rutgers University, New Brunswick, New Jersey"],"affiliations":[{"raw_affiliation_string":"Rutcor-Rutgers Center For Or Rutgers University, New Brunswick, New Jersey","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100342208"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.4967,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66389987,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"3","first_page":"235","last_page":"249"},"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/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994999766349792,"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/mathematics","display_name":"Mathematics","score":0.8268677592277527},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6730263233184814},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5685187578201294},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48312613368034363},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.44031861424446106},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.43765968084335327},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.33954310417175293}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8268677592277527},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6730263233184814},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5685187578201294},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48312613368034363},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.44031861424446106},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.43765968084335327},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.33954310417175293}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190150302","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190150302","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":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W87819546","https://openalex.org/W119366631","https://openalex.org/W149789455","https://openalex.org/W1484040084","https://openalex.org/W1543425397","https://openalex.org/W1967909723","https://openalex.org/W1974534721","https://openalex.org/W1985076392","https://openalex.org/W1988103993","https://openalex.org/W1988405963","https://openalex.org/W1993229752","https://openalex.org/W1995835364","https://openalex.org/W1996803865","https://openalex.org/W1999384664","https://openalex.org/W2000424945","https://openalex.org/W2000506665","https://openalex.org/W2010277027","https://openalex.org/W2019029270","https://openalex.org/W2022429180","https://openalex.org/W2032198396","https://openalex.org/W2034008483","https://openalex.org/W2042324334","https://openalex.org/W2047899424","https://openalex.org/W2064721098","https://openalex.org/W2068683531","https://openalex.org/W2077863743","https://openalex.org/W2092353941","https://openalex.org/W2127470768","https://openalex.org/W2143474538","https://openalex.org/W2157783000","https://openalex.org/W2163648032","https://openalex.org/W2164793044","https://openalex.org/W2314893179","https://openalex.org/W4210396282","https://openalex.org/W4213070679","https://openalex.org/W4239569302","https://openalex.org/W4240884087","https://openalex.org/W4241927515","https://openalex.org/W4299866835","https://openalex.org/W4301216918","https://openalex.org/W6635564327","https://openalex.org/W6647236097","https://openalex.org/W6655258860","https://openalex.org/W6758373158"],"related_works":["https://openalex.org/W1493471320","https://openalex.org/W2791860840","https://openalex.org/W2046928120","https://openalex.org/W1593455592","https://openalex.org/W1931833622","https://openalex.org/W2035649640","https://openalex.org/W4299906858","https://openalex.org/W2606892216","https://openalex.org/W4385659976","https://openalex.org/W2079272435"],"abstract_inverted_index":{"Abstract":[0],"The":[1,25],"threshold":[2,23,26,33,49,73],"weight":[3,50,74],"of":[4,13,44,75,89,92,95,123],"a":[5,11,22,84,93,102,108,118],"graph":[6,86,103,120],"G":[7,18],"is":[8,41,51],"introduced":[9],"as":[10,59,66,115],"measure":[12],"the":[14,30,38,42,48,52,63,72,90],"amount":[15],"by":[16],"which":[17,47],"differs":[19],"from":[20],"being":[21],"graph.":[24],"graphs":[27,31,45,56],"are":[28,35,57,65],"precisely":[29],"whose":[32],"weights":[34],"0.":[36],"At":[37],"opposite":[39],"extreme":[40],"class":[43],"for":[46,83,101,117],"maximum":[53],"possible.":[54],"Such":[55],"defined":[58],"heavy":[60,85,106,119],"graphs.":[61],"Among":[62],"results":[64],"following:":[67],"A":[68],"theorem":[69],"that":[70],"specifies":[71],"any":[76],"triangle\u2010free":[77],"graph;":[78],"necessary":[79,109],"and":[80,107],"sufficient":[81,99],"conditions":[82,100],"in":[87,121],"terms":[88,122],"solvability":[91],"system":[94],"linear":[96],"inequalities;":[97],"some":[98],"to":[104,112],"be":[105,113],"condition":[110],"(conjectured":[111],"sufficient,":[114],"well)":[116],"its":[124],"cliques.":[125]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}