{"id":"https://openalex.org/W1599973946","doi":"https://doi.org/10.37236/213","title":"The Excessive [3]-Index of All Graphs","display_name":"The Excessive [3]-Index of All Graphs","publication_year":2009,"publication_date":"2009-10-05","ids":{"openalex":"https://openalex.org/W1599973946","doi":"https://doi.org/10.37236/213","mag":"1599973946"},"language":"en","primary_location":{"id":"doi:10.37236/213","is_oa":true,"landing_page_url":"https://doi.org/10.37236/213","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r124/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/v16i1r124/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082977996","display_name":"David Cariolaro","orcid":null},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"David Cariolaro","raw_affiliation_strings":["Xi\u2032an Jiaotong Liverpool University"],"affiliations":[{"raw_affiliation_string":"Xi\u2032an Jiaotong Liverpool University","institution_ids":["https://openalex.org/I69356397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008893362","display_name":"Hung\u2010Lin Fu","orcid":"https://orcid.org/0000-0001-7218-3043"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hung-Lin Fu","raw_affiliation_strings":["Department of Applied Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082977996"],"corresponding_institution_ids":["https://openalex.org/I69356397"],"apc_list":null,"apc_paid":null,"fwci":0.707,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.69095728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9968000054359436,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9965999722480774,"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":0.877947211265564},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7829203009605408},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6427139043807983},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3680616021156311}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.877947211265564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7829203009605408},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6427139043807983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3680616021156311}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/213","is_oa":true,"landing_page_url":"https://doi.org/10.37236/213","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r124/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:CiteSeerX.psu:10.1.1.173.3718","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.173.3718","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sinica.edu.tw/post-doctor/cariolaro/com33_s.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.5372","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.5372","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r124.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/213","is_oa":true,"landing_page_url":"https://doi.org/10.37236/213","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r124/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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1599973946.pdf","grobid_xml":"https://content.openalex.org/works/W1599973946.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W123929782","https://openalex.org/W1632512299","https://openalex.org/W1980551257","https://openalex.org/W2021614430","https://openalex.org/W2059608229","https://openalex.org/W2097849377","https://openalex.org/W2569119448","https://openalex.org/W4230518595","https://openalex.org/W4233756358"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2582950667","https://openalex.org/W1527576459","https://openalex.org/W2622512907","https://openalex.org/W1596060973","https://openalex.org/W2028852147","https://openalex.org/W2765245303","https://openalex.org/W2989925696","https://openalex.org/W2183745707","https://openalex.org/W3003396734"],"abstract_inverted_index":{"Let":[0],"$m$":[1,127,138],"be":[2,9],"a":[3,10,70,141,155],"positive":[4],"integer":[5],"and":[6,62,76,103,128,140],"let":[7],"$G$":[8,31,36,61,90,129],"graph.":[11],"A":[12],"set":[13,86],"${\\cal":[14,47],"M}$":[15,48],"of":[16,18,21,23,30,60,65,82,122],"matchings":[17,66],"$G$,":[19,102],"all":[20,165],"which":[22],"size":[24],"$m$,":[25],"is":[26,37,53,55,69,84,91,95,105,147],"called":[27,38,56,73],"an":[28,43,57],"$[m]$-covering":[29,46],"if":[32,40,89],"$\\bigcup_{M\\in":[33],"{{\\cal":[34],"M}}}M=E(G)$.":[35],"$[m]$-coverable":[39],"it":[41,67,104],"has":[42],"$[m]$-covering.":[44],"An":[45],"such":[49,154],"that":[50,97,110],"$|{{\\cal":[51],"M}}|$":[52],"minimum":[54],"excessive":[58,74,162],"$[m]$-factorization":[59],"the":[63,120,161],"number":[64],"contains":[68],"graph":[71,101,117],"parameter":[72],"$[m]$-index":[75],"denoted":[77],"by":[78],"$\\chi'_{[m]}(G)$":[79,83,124],"(the":[80],"value":[81],"conventionally":[85],"to":[87,108,131],"$\\infty$":[88],"not":[92,106],"$[m]$-coverable).":[93],"It":[94],"obvious":[96],"$\\chi'_{[1]}(G)=|E(G)|$":[98],"for":[99,114,125,144,157,164],"every":[100,115],"difficult":[107],"see":[109],"$\\chi'_{[2]}(G)=\\max\\{\\chi'(G),\\lceil":[111],"|E(G)|/2":[112],"\\rceil\\}$":[113],"$[2]$-coverable":[116],"$G$.":[118],"However":[119],"task":[121],"determining":[123,160],"arbitrary":[126],"seems":[130],"increase":[132],"very":[133],"rapidly":[134],"in":[135],"difficulty":[136],"as":[137],"increases,":[139],"general":[142],"formula":[143,156],"$m\\geq":[145],"3$":[146],"unknown.":[148],"In":[149],"this":[150],"paper":[151],"we":[152],"determine":[153],"$m=3,$":[158],"thereby":[159],"$[3]$-index":[163],"graphs.":[166]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
