{"id":"https://openalex.org/W2086829022","doi":"https://doi.org/10.1080/00207160902777914","title":"A sufficient condition for a graph to be an (<i>a, b, k</i>)-critical graph","display_name":"A sufficient condition for a graph to be an (<i>a, b, k</i>)-critical graph","publication_year":2010,"publication_date":"2010-06-17","ids":{"openalex":"https://openalex.org/W2086829022","doi":"https://doi.org/10.1080/00207160902777914","mag":"2086829022"},"language":"en","primary_location":{"id":"doi:10.1080/00207160902777914","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160902777914","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5101764220","display_name":"Sizhong Zhou","orcid":"https://orcid.org/0000-0003-2093-2158"},"institutions":[{"id":"https://openalex.org/I4210096899","display_name":"Jiangsu University of Science and Technology","ror":"https://ror.org/00tyjp878","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210096899"]},{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sizhong Zhou","raw_affiliation_strings":["School of Mathematics and Physics , Jiangsu University of Science and Technology , Mengxi Road 2, Zhenjiang, Jiangsu, 212003, China","School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics , Jiangsu University of Science and Technology , Mengxi Road 2, Zhenjiang, Jiangsu, 212003, China","institution_ids":["https://openalex.org/I4210096899"]},{"raw_affiliation_string":"School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China#TAB#","institution_ids":["https://openalex.org/I115592961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101764220"],"corresponding_institution_ids":["https://openalex.org/I115592961","https://openalex.org/I4210096899"],"apc_list":null,"apc_paid":null,"fwci":2.6762,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.89958969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"87","issue":"10","first_page":"2202","last_page":"2211"},"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":0.9997000098228455,"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/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"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":0.7563079595565796},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.691184937953949},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.5983060002326965},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5410169363021851},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.5324434041976929},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.5089263916015625},{"id":"https://openalex.org/keywords/vertex-transitive-graph","display_name":"Vertex-transitive graph","score":0.49831247329711914},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49518266320228577},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.4940105080604553},{"id":"https://openalex.org/keywords/factor-critical-graph","display_name":"Factor-critical graph","score":0.4862781763076782},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.4767771065235138},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.4672384560108185},{"id":"https://openalex.org/keywords/distance-regular-graph","display_name":"Distance-regular graph","score":0.4558687210083008},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.435005247592926},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4295233190059662}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7563079595565796},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.691184937953949},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.5983060002326965},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5410169363021851},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.5324434041976929},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.5089263916015625},{"id":"https://openalex.org/C113203676","wikidata":"https://www.wikidata.org/wiki/Q220997","display_name":"Vertex-transitive graph","level":5,"score":0.49831247329711914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49518266320228577},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.4940105080604553},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.4862781763076782},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.4767771065235138},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.4672384560108185},{"id":"https://openalex.org/C56783289","wikidata":"https://www.wikidata.org/wiki/Q3115556","display_name":"Distance-regular graph","level":5,"score":0.4558687210083008},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.435005247592926},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4295233190059662}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160902777914","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160902777914","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320327794","display_name":"Qinglan Project of Jiangsu Province of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W403078265","https://openalex.org/W1484040084","https://openalex.org/W1963496295","https://openalex.org/W1970805731","https://openalex.org/W1978366995","https://openalex.org/W1987223948","https://openalex.org/W1996149838","https://openalex.org/W2027460894","https://openalex.org/W2117338875","https://openalex.org/W2153983222","https://openalex.org/W2376203023","https://openalex.org/W2401701830","https://openalex.org/W3144266635"],"related_works":["https://openalex.org/W2364074136","https://openalex.org/W2760415759","https://openalex.org/W4290651641","https://openalex.org/W4254020973","https://openalex.org/W4213457879","https://openalex.org/W2404212820","https://openalex.org/W921027354","https://openalex.org/W587376096","https://openalex.org/W2765806635","https://openalex.org/W2086829022"],"abstract_inverted_index":{"Let":[0],"G":[1,20,29,41,56,61,82],"be":[2,10,84],"a":[3,24,39,69,76,80],"graph,":[4],"and":[5],"let":[6],"a,":[7],"b,":[8,46,87],"k":[9,53],"integers":[11],"with":[12],"0\u2264a\u2264b,":[13],"k\u22650.":[14],"An":[15],"[a,":[16,64],"b]-factor":[17],"of":[18,28,55,60],"graph":[19,40,48,59,81],"is":[21,42,72,75],"defined":[22],"as":[23],"spanning":[25],"subgraph":[26],"F":[27,33],"such":[30],"that":[31],"a\u2264d":[32],"(x)\u2264b":[34],"for":[35,79],"each":[36],"x\u2208V(G).":[37],"Then":[38],"called":[43],"an":[44,63,85],"(a,":[45,86],"k)-critical":[47,88],"if":[49],"after":[50],"deleting":[51],"any":[52],"vertices":[54],"the":[57],"remaining":[58],"has":[62],"b]-factor.":[65],"In":[66],"this":[67],"article,":[68],"sufficient":[70],"condition":[71,78],"given,":[73],"which":[74],"neighborhood":[77],"to":[83],"graph.":[89]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
