{"id":"https://openalex.org/W1488677252","doi":"https://doi.org/10.37236/1972","title":"A Note on Graphs Without Short Even Cycles","display_name":"A Note on Graphs Without Short Even Cycles","publication_year":2005,"publication_date":"2005-04-06","ids":{"openalex":"https://openalex.org/W1488677252","doi":"https://doi.org/10.37236/1972","mag":"1488677252"},"language":"en","primary_location":{"id":"doi:10.37236/1972","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1972","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n5/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079339565","display_name":"Thomas Lam","orcid":"https://orcid.org/0000-0003-2346-7685"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Thomas Lam","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cam-bridge, MA 02139, USA","Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cam-bridge, MA 02139, USA","institution_ids":[]},{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024446850","display_name":"Jacques Verstra\u00ebte","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jacques Verstra\u00ebte","raw_affiliation_strings":["(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079339565"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.01,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.75484831,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"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":0.9998000264167786,"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":0.9987999796867371,"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":0.8448394536972046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8428720235824585},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5981778502464294},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5049362778663635},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4344973862171173},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39365702867507935}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8448394536972046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8428720235824585},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5981778502464294},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5049362778663635},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4344973862171173},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39365702867507935}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1972","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1972","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.5442","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.5442","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0503623v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.1381","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.1381","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_12/PDF/v12i1n5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1972","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1972","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1488677252.pdf","grobid_xml":"https://content.openalex.org/works/W1488677252.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1199371048","https://openalex.org/W1515707356","https://openalex.org/W1548164611","https://openalex.org/W1582742149","https://openalex.org/W1965909513","https://openalex.org/W1987996179","https://openalex.org/W2011039300","https://openalex.org/W2051660589","https://openalex.org/W2058374373","https://openalex.org/W2087806988","https://openalex.org/W2091972153","https://openalex.org/W2093219044","https://openalex.org/W2110805362","https://openalex.org/W2479778494","https://openalex.org/W2611185757","https://openalex.org/W2913343784","https://openalex.org/W6655579563"],"related_works":["https://openalex.org/W1964910584","https://openalex.org/W1522469957","https://openalex.org/W2152925324","https://openalex.org/W30750922","https://openalex.org/W1719252778","https://openalex.org/W2038397650","https://openalex.org/W2983736839","https://openalex.org/W2374778222","https://openalex.org/W2079890680","https://openalex.org/W1731368709"],"abstract_inverted_index":{"In":[0],"this":[1,34],"note,":[2],"we":[3],"show":[4,32],"that":[5,33],"any":[6],"$n$-vertex":[7],"graph":[8],"without":[9],"even":[10],"cycles":[11],"of":[12,29],"length":[13],"at":[14,18],"most":[15,19],"$2k$":[16],"has":[17],"${1\\over2}n^{1":[20],"+":[21,23],"1/k}":[22],"O(n)$":[24],"edges,":[25],"and":[26],"polarity":[27],"graphs":[28],"generalized":[30],"polygons":[31],"is":[35],"asymptotically":[36],"tight":[37],"when":[38],"$k":[39],"\\in":[40],"\\{2,3,5\\}$.":[41]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
