{"id":"https://openalex.org/W2023176270","doi":"https://doi.org/10.1137/110834408","title":"A Chain Theorem for $3^+$-Connected Graphs","display_name":"A Chain Theorem for $3^+$-Connected Graphs","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2023176270","doi":"https://doi.org/10.1137/110834408","mag":"2023176270"},"language":"en","primary_location":{"id":"doi:10.1137/110834408","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110834408","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete 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/A5108454863","display_name":"Guoli Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guoli Ding","raw_affiliation_strings":["ding@math.lsu.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"ding@math.lsu.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047791836","display_name":"Liu Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng Liu","raw_affiliation_strings":["liuchengmath@163.com#TAB#"],"affiliations":[{"raw_affiliation_string":"liuchengmath@163.com#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108454863"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6739,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69996387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"1","first_page":"102","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9923999905586243,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9883000254631042,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8115666508674622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7451115846633911},{"id":"https://openalex.org/keywords/graph-minor","display_name":"Graph minor","score":0.6049747467041016},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5134488344192505},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.503093421459198},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.47963935136795044},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.4375859797000885},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4171912670135498},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.34019166231155396},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.2588801980018616}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8115666508674622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7451115846633911},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.6049747467041016},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5134488344192505},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.503093421459198},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.47963935136795044},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.4375859797000885},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4171912670135498},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.34019166231155396},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.2588801980018616}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110834408","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110834408","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1388","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/389","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1388","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/389","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W221616633","https://openalex.org/W1964757115","https://openalex.org/W1994560437","https://openalex.org/W2040101882","https://openalex.org/W2048453235","https://openalex.org/W2048456408","https://openalex.org/W2057873207","https://openalex.org/W2068725754","https://openalex.org/W2071321409","https://openalex.org/W2072616272","https://openalex.org/W2912381149"],"related_works":["https://openalex.org/W2606892216","https://openalex.org/W2046928120","https://openalex.org/W4298570565","https://openalex.org/W2248185380","https://openalex.org/W2963157799","https://openalex.org/W2949755351","https://openalex.org/W4301695108","https://openalex.org/W1991938654","https://openalex.org/W2968937615","https://openalex.org/W2762578128"],"abstract_inverted_index":{"A":[0],"3-connected":[1],"graph":[2,36],"is":[3,25,43,55,63],"called":[4],"$3^+$-connected":[5,35,39],"if":[6],"it":[7],"has":[8,37],"no":[9],"3-separation":[10],"that":[11,30,42],"separates":[12],"a":[13,38],"\u201clarge\u201d":[14],"fan":[15],"or":[16],"$K_{3,n}$":[17],"from":[18,49,65],"the":[19,22,50,66],"rest":[20],"of":[21],"graph.":[23,52],"It":[24],"proved":[26],"in":[27],"this":[28],"paper":[29],"except":[31],"for":[32],"$K_4$,":[33],"every":[34],"proper":[40],"minor":[41],"at":[44],"most":[45],"two":[46],"edges":[47],"away":[48],"original":[51],"This":[53],"result":[54],"used":[56],"to":[57],"characterize":[58],"Q-minor-free":[59],"graphs,":[60],"where":[61],"Q":[62],"obtained":[64],"cube":[67],"by":[68],"contracting":[69],"an":[70],"edge.":[71]},"counts_by_year":[{"year":2015,"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"}
