{"id":"https://openalex.org/W2004979475","doi":"https://doi.org/10.1007/s00373-004-0558-z","title":"The Toughness of a Toroidal Graph with Connectivity 3 and Girth 6 is Exactly 1","display_name":"The Toughness of a Toroidal Graph with Connectivity 3 and Girth 6 is Exactly 1","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W2004979475","doi":"https://doi.org/10.1007/s00373-004-0558-z","mag":"2004979475"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-004-0558-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-004-0558-z","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","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/A5056108777","display_name":"Weiting Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weiting Cao","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, IL 61801, USA","University of Illinois, Department of Mathematics, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois, Department of Mathematics, USA#TAB#","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068581962","display_name":"Michael J. Pelsmajer","orcid":"https://orcid.org/0000-0001-9688-5787"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael J. Pelsmajer","raw_affiliation_strings":["Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA","Illinois Institute of Technology, Department of Applied Mathematics, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":"Illinois Institute of Technology, Department of Applied Mathematics, USA#TAB#","institution_ids":["https://openalex.org/I180949307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068581962"],"corresponding_institution_ids":["https://openalex.org/I180949307"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11535937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"20","issue":"2","first_page":"181","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9997000098228455,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.7218382358551025},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7218075394630432},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6779137253761292},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6527003049850464},{"id":"https://openalex.org/keywords/toroid","display_name":"Toroid","score":0.5621718168258667},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5349624752998352},{"id":"https://openalex.org/keywords/toughness","display_name":"Toughness","score":0.47975313663482666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44402816891670227},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.4112558662891388},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2272435426712036},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13663601875305176},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.06294861435890198},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.04312103986740112}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7218382358551025},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7218075394630432},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6779137253761292},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6527003049850464},{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.5621718168258667},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5349624752998352},{"id":"https://openalex.org/C99595764","wikidata":"https://www.wikidata.org/wiki/Q486802","display_name":"Toughness","level":2,"score":0.47975313663482666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44402816891670227},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.4112558662891388},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2272435426712036},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13663601875305176},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06294861435890198},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.04312103986740112},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-004-0558-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-004-0558-z","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1974731924","https://openalex.org/W1975099798","https://openalex.org/W2026704910"],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W2077383796","https://openalex.org/W2080136900","https://openalex.org/W2372768926","https://openalex.org/W2999799752","https://openalex.org/W2054458431","https://openalex.org/W3013576436","https://openalex.org/W1655253263","https://openalex.org/W2384730381"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
