{"id":"https://openalex.org/W2883406596","doi":"https://doi.org/10.23638/dmtcs-21-3-1","title":"Binding Number, Toughness and General Matching Extendability in Graphs","display_name":"Binding Number, Toughness and General Matching Extendability in Graphs","publication_year":2019,"publication_date":"2019-01-17","ids":{"openalex":"https://openalex.org/W2883406596","doi":"https://doi.org/10.23638/dmtcs-21-3-1","mag":"2883406596"},"language":"en","primary_location":{"id":"doi:10.23638/dmtcs-21-3-1","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-3-1","pdf_url":"https://dmtcs.episciences.org/5091/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/5091/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009504144","display_name":"Hongliang Lu","orcid":"https://orcid.org/0000-0003-4447-2416"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hongliang Lu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061432086","display_name":"Qinglin Yu","orcid":"https://orcid.org/0000-0002-0847-7669"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qinglin Yu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009504144"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0181088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Vol. 21 no. 3","issue":"Graph Theory","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":0.9983999729156494,"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":0.9983999729156494,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.8805699348449707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7776874303817749},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6676688194274902},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6334202289581299},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5686810612678528},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5434085130691528},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36721736192703247}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8805699348449707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7776874303817749},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6676688194274902},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6334202289581299},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5686810612678528},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5434085130691528},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36721736192703247},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.23638/dmtcs-21-3-1","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-3-1","pdf_url":"https://dmtcs.episciences.org/5091/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.11159","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.11159","pdf_url":"https://arxiv.org/pdf/1807.11159","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1807.11159","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1807.11159","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/dmtcs-21-3-1","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-3-1","pdf_url":"https://dmtcs.episciences.org/5091/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1304196372","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5238242616","display_name":null,"funder_award_id":"11871391","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6058138561","display_name":null,"funder_award_id":", No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7346218018","display_name":null,"funder_award_id":"11871","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7608752429","display_name":null,"funder_award_id":"Talent","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7741647303","display_name":null,"funder_award_id":"11471257","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2883406596.pdf","grobid_xml":"https://content.openalex.org/works/W2883406596.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2015539907","https://openalex.org/W2091978516"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4256429076","https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W2348092930","https://openalex.org/W2012063272","https://openalex.org/W3129272755","https://openalex.org/W2138685729","https://openalex.org/W1968154277","https://openalex.org/W1553466895"],"abstract_inverted_index":{"A":[0],"connected":[1,58],"graph":[2,59,110,122],"$G$":[3,48,123,133,144,150],"with":[4,34,60,124],"at":[5,61],"least":[6,62],"$2m":[7],"+":[8,10],"2n":[9],"2$":[11],"vertices":[12,64],"which":[13],"contains":[14,88],"a":[15,43,57,89,95,109,146],"perfect":[16,44,90,187],"matching":[17,45,80,175],"is":[18,42,65,134,151,157],"$E(m,":[19],"n)$-{\\it":[20],"extendable},":[21],"if":[22,69,129,140],"for":[23,70,120,169,183],"any":[24,71,79],"two":[25,113],"sets":[26],"of":[27,75,82,85,108,116,172,186],"disjoint":[28],"independent":[29],"edges":[30],"$M$":[31,81],"and":[32,38,53,78,100,106,136,143,153,166],"$N$":[33],"$|M|":[35],"=":[36],"m$":[37],"$|N|=":[39],"n$,":[40],"there":[41],"$F$":[46],"in":[47],"such":[49],"that":[50,162,182],"$M\\subseteq":[51],"F$":[52],"$N\\cap":[54],"F=\\emptyset$.":[55],"Similarly,":[56],"$n+2k+2$":[63],"called":[66],"$(n,k)$-{\\it":[67],"extendable}":[68],"vertex":[72],"set":[73],"$S$":[74],"size":[76,83],"$n$":[77],"$k$":[84],"$G-S$,":[86],"$G-S-V(M)$":[87],"matching.":[91],"Let":[92],"$\\varepsilon$":[93],"be":[94,102],"small":[96],"positive":[97],"constant,":[98],"$b(G)$":[99],"$t(G)$":[101],"the":[103,163,170,173,184],"binding":[104,164],"number":[105,165],"toughness":[107,167],"$G$.":[111],"The":[112],"main":[114],"theorems":[115],"this":[117],"paper":[118],"are:":[119],"every":[121],"sufficiently":[125],"large":[126],"order,":[127],"1)":[128],"$b(G)\\geq":[130],"4/3+\\varepsilon$,":[131],"then":[132,149],"$E(m,n)$-extendable":[135,152],"also":[137,154],"$(n,k)$-extendable;":[138],"2)":[139],"$t(G)\\geq":[141],"1+\\varepsilon$":[142],"has":[145],"high":[147],"connectivity,":[148],"$(n,k)$-extendable.":[155],"It":[156],"worth":[158],"to":[159],"point":[160],"out":[161],"conditions":[168],"existence":[171,185],"general":[174],"extension":[176],"properties":[177],"are":[178],"almost":[179],"same":[180],"as":[181],"matchings.":[188],"Comment:":[189],"10":[190],"pages":[191]},"counts_by_year":[],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}
