{"id":"https://openalex.org/W2039267480","doi":"https://doi.org/10.1137/090767868","title":"Computing the Girth of a Planar Graph in $O(n \\logn)$ Time","display_name":"Computing the Girth of a Planar Graph in $O(n \\logn)$ Time","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2039267480","doi":"https://doi.org/10.1137/090767868","mag":"2039267480"},"language":"en","primary_location":{"id":"doi:10.1137/090767868","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090767868","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/A5000569191","display_name":"Oren Weimann","orcid":"https://orcid.org/0000-0002-4510-7552"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oren Weimann","raw_affiliation_strings":["oren.weimann@weizmann.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"oren.weimann@weizmann.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":["raphy@math.haifa.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"raphy@math.haifa.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0148,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.76769593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"2","first_page":"609","last_page":"616"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980999827384949,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8145574927330017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7329542636871338},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6232283711433411},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.5768555402755737},{"id":"https://openalex.org/keywords/butterfly-graph","display_name":"Butterfly graph","score":0.575100302696228},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4754595160484314},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47509682178497314},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.45942074060440063},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.45584553480148315},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.4416179955005646},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4411211311817169},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20729276537895203},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.1721612513065338}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8145574927330017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7329542636871338},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6232283711433411},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.5768555402755737},{"id":"https://openalex.org/C18819970","wikidata":"https://www.wikidata.org/wiki/Q3035340","display_name":"Butterfly graph","level":5,"score":0.575100302696228},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4754595160484314},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47509682178497314},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.45942074060440063},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.45584553480148315},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.4416179955005646},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4411211311817169},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20729276537895203},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.1721612513065338},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090767868","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090767868","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W146202307","https://openalex.org/W1527709704","https://openalex.org/W1966874927","https://openalex.org/W1967066104","https://openalex.org/W1991858502","https://openalex.org/W1999497750","https://openalex.org/W2002722727","https://openalex.org/W2036489778","https://openalex.org/W2038643780","https://openalex.org/W2064153357","https://openalex.org/W2065759448","https://openalex.org/W2065796538","https://openalex.org/W2067431706","https://openalex.org/W2072487438","https://openalex.org/W2073558110","https://openalex.org/W2083049364","https://openalex.org/W2087083200","https://openalex.org/W2092904196","https://openalex.org/W2093962232","https://openalex.org/W2094724468","https://openalex.org/W2131676402","https://openalex.org/W2161439427","https://openalex.org/W2296148711","https://openalex.org/W2762935521","https://openalex.org/W2798588639","https://openalex.org/W3004540582","https://openalex.org/W3145128584","https://openalex.org/W4229970255"],"related_works":["https://openalex.org/W2802636101","https://openalex.org/W2039281885","https://openalex.org/W3192131378","https://openalex.org/W1539438692","https://openalex.org/W1501403775","https://openalex.org/W4290720427","https://openalex.org/W4248954595","https://openalex.org/W2016898545","https://openalex.org/W2964695382","https://openalex.org/W2351009969"],"abstract_inverted_index":{"We":[0],"give":[1],"an":[2,13],"$O(n\\log":[3],"n)$":[4],"algorithm":[5],"for":[6,35],"computing":[7],"the":[8,30],"girth":[9],"(shortest":[10],"cycle)":[11],"of":[12,24],"undirected":[14],"n-vertex":[15],"planar":[16],"graph.":[17],"Our":[18],"solution":[19],"extends":[20],"to":[21],"any":[22],"graph":[23],"bounded":[25],"genus.":[26],"This":[27],"improves":[28],"upon":[29],"best":[31],"previously":[32],"known":[33],"algorithms":[34],"this":[36],"problem.":[37]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
