{"id":"https://openalex.org/W2095368348","doi":"https://doi.org/10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.0.co;2-n","title":"On a conjecture of Thomassen and Toft","display_name":"On a conjecture of Thomassen and Toft","publication_year":1999,"publication_date":"1999-10-01","ids":{"openalex":"https://openalex.org/W2095368348","doi":"https://doi.org/10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.0.co;2-n","mag":"2095368348"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.0.co;2-n","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/A5037836325","display_name":"Matthias Kriesell","orcid":"https://orcid.org/0000-0002-7302-7496"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Kriesell","raw_affiliation_strings":["Institut f. Mathematik (A), Universita\u0308t Hannover, Welfengarten 1, D-30167 Hannover, Germany","Institut f. Mathematik (A), Universit\u00e4t Hannover, Welfengarten 1, D-30167 Hannover, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f. Mathematik (A), Universita\u0308t Hannover, Welfengarten 1, D-30167 Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]},{"raw_affiliation_string":"Institut f. Mathematik (A), Universit\u00e4t Hannover, Welfengarten 1, D-30167 Hannover, Germany#TAB#","institution_ids":["https://openalex.org/I114112103"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037836325"],"corresponding_institution_ids":["https://openalex.org/I114112103"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22243248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"2","first_page":"118","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9987000226974487,"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":0.9797000288963318,"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":0.8201771974563599},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.784497082233429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.773934006690979},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6315421462059021},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49604567885398865},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.45821020007133484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.350333034992218}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8201771974563599},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.784497082233429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.773934006690979},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6315421462059021},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49604567885398865},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.45821020007133484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.350333034992218},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.0.co;2-n","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"},{"id":"doi:10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.3.co;2-e","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199910)32:2<118::aid-jgt2>3.3.co;2-e","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"},{"id":"mag:2095368348","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/jgt/jgt32.html#Kriesell99","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":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of Graph Theory","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2067458708"],"related_works":["https://openalex.org/W2081681676","https://openalex.org/W2075196560","https://openalex.org/W2045535364","https://openalex.org/W2914928947","https://openalex.org/W1987826317","https://openalex.org/W2003281578","https://openalex.org/W1966188437","https://openalex.org/W2186983195","https://openalex.org/W2026750191","https://openalex.org/W2013509986","https://openalex.org/W2947185854","https://openalex.org/W2150726531","https://openalex.org/W2506159978","https://openalex.org/W2022421239","https://openalex.org/W3147950827","https://openalex.org/W2377252232","https://openalex.org/W2118360213","https://openalex.org/W2185264966","https://openalex.org/W2087420573","https://openalex.org/W1985032817"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2,101,126],"motivated":[3],"by":[4],"a":[5,32,79],"conjecture":[6],"of":[7,15,19,26,28,40,53,55,78],"Thomassen":[8,59,65],"and":[9,22,60],"Toft":[10,61],"on":[11],"the":[12,23,37,51,56,76],"number":[13,24,52],"s2(G)":[14,84,113],"separating":[16],"vertex":[17],"sets":[18],"cardinality":[20],"2":[21,30],"\u03c52(G)":[25,86,115],"vertices":[27],"degree":[29],"in":[31,63,104],"graph":[33,57],"G":[34,93,122],"belonging":[35],"to":[36,108],"class":[38],"\ud835\udca2":[39],"all":[41,92,120],"2-connected":[42],"graphs":[43],"without":[44],"nonseparating":[45],"induced":[46],"cycles.":[47],"Let":[48],"\u2016G\u2016":[49,90,118],"denote":[50],"edges":[54],"G.":[58],"conjectured":[62],"[C.":[64],"&":[66,132],"B.":[67],"Toft,":[68],"J.":[69],"Combin.":[70],"Theory":[71,137],"B":[72],"31":[73],"(1981),":[74],"199\u2013224]":[75],"existence":[77],"positive":[80],"constant":[81],"c":[82,88],"satisfying":[83],"+":[85,114],">":[87,116],"\u00b7":[89,117],"for":[91,119],"\u2208":[94,123],"\ud835\udca2.":[95],"We":[96],"shall":[97],"see":[98],"that":[99],"this":[100],"not":[102],"true":[103],"general.":[105],"Restricting":[106],"ourselves":[107],"planar":[109,121],"graphs,":[110],"we":[111],"obtain":[112],"\ud835\udca2,":[124],"where":[125],"best-possible.":[127],"\u00a9":[128],"1999":[129,140],"John":[130],"Wiley":[131],"Sons,":[133],"Inc.":[134],"J":[135],"Graph":[136],"32:":[138],"118\u2013122,":[139]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
