{"id":"https://openalex.org/W2028299806","doi":"https://doi.org/10.1142/s1793830909000038","title":"WHEN DO THREE LONGEST PATHS HAVE A COMMON VERTEX?","display_name":"WHEN DO THREE LONGEST PATHS HAVE A COMMON VERTEX?","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2028299806","doi":"https://doi.org/10.1142/s1793830909000038","mag":"2028299806"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830909000038","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830909000038","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5079004436","display_name":"Maria Axenovich","orcid":"https://orcid.org/0000-0002-8843-9557"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"MARIA AXENOVICH","raw_affiliation_strings":["412 Carver Hall, Iowa State University, Ames, IA 50011, USA"],"affiliations":[{"raw_affiliation_string":"412 Carver Hall, Iowa State University, Ames, IA 50011, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079004436"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":0.707,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.70774431,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"01","issue":"01","first_page":"115","last_page":"120"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","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/T11476","display_name":"Graph theory and applications","score":0.9975000023841858,"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":0.8221988677978516},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6584211587905884},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6037242412567139},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5782386064529419},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44019076228141785},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4372212886810303},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.42387276887893677},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4155414402484894},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.32013410329818726},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.18287557363510132}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8221988677978516},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6584211587905884},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6037242412567139},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5782386064529419},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44019076228141785},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4372212886810303},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.42387276887893677},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4155414402484894},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.32013410329818726},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.18287557363510132}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s1793830909000038","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830909000038","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.296.4358","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.4358","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.kit.edu/iag6/~axenovich/media/path-trans.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.530.771","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.530.771","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://orion.math.iastate.edu/axenovic/Papers/Path-Transversals.pdf","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":3,"referenced_works":["https://openalex.org/W2015549411","https://openalex.org/W2073695625","https://openalex.org/W2172129783"],"related_works":["https://openalex.org/W1554245510","https://openalex.org/W2125939925","https://openalex.org/W2910018628","https://openalex.org/W2008957319","https://openalex.org/W2766499403","https://openalex.org/W2497554862","https://openalex.org/W2963206482","https://openalex.org/W4293002939","https://openalex.org/W4234165247","https://openalex.org/W1551301028"],"abstract_inverted_index":{"It":[0,16,35],"is":[1,17],"well":[2],"known":[3,19],"that":[4,20,38],"any":[5,39],"two":[6],"longest":[7,27,41],"paths":[8,28,42],"in":[9,43,50,71],"a":[10,14,32,44,48],"connected":[11,23,45],"graph":[12,46],"share":[13,31],"vertex.":[15,34],"also":[18],"there":[21],"are":[22],"graphs":[24,61],"where":[25],"7":[26],"do":[29],"not":[30],"common":[33],"was":[36],"conjectured":[37],"three":[40],"have":[47],"vertex":[49],"common.":[51],"In":[52],"this":[53],"note":[54],"we":[55],"prove":[56],"the":[57,67],"conjecture":[58,68],"for":[59,66],"outerplanar":[60],"and":[62],"give":[63],"sufficient":[64],"conditions":[65],"to":[69],"hold":[70],"general.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}