{"id":"https://openalex.org/W2108615664","doi":"https://doi.org/10.37236/1665","title":"A Proof of the Two-path Conjecture","display_name":"A Proof of the Two-path Conjecture","publication_year":2002,"publication_date":"2002-03-13","ids":{"openalex":"https://openalex.org/W2108615664","doi":"https://doi.org/10.37236/1665","mag":"2108615664"},"language":"en","primary_location":{"id":"doi:10.37236/1665","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1665","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1n4/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1n4/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088309054","display_name":"Herbert Fleischner","orcid":"https://orcid.org/0000-0001-8588-5212"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Herbert Fleischner","raw_affiliation_strings":["Institute of Discrete Mathematics Austrian Academy of Sciences Sonnenfelsgasse 19 A-1010 Vienna Austria, EU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics Austrian Academy of Sciences Sonnenfelsgasse 19 A-1010 Vienna Austria, EU","institution_ids":["https://openalex.org/I138211613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002646314","display_name":"Robert Molina","orcid":null},"institutions":[{"id":"https://openalex.org/I186589156","display_name":"Alma College","ror":"https://ror.org/02pdzen98","country_code":"US","type":"education","lineage":["https://openalex.org/I186589156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert R. Molina","raw_affiliation_strings":["Department of Mathematics and Computer Science Alma College 614 W. Superior St. Alma MI, 48801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science Alma College 614 W. Superior St. Alma MI, 48801","institution_ids":["https://openalex.org/I186589156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090201337","display_name":"K. Smith","orcid":"https://orcid.org/0000-0001-9535-3199"},"institutions":[{"id":"https://openalex.org/I1629065","display_name":"Central Michigan University","ror":"https://ror.org/02xawj266","country_code":"US","type":"education","lineage":["https://openalex.org/I1629065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ken W. Smith","raw_affiliation_strings":["Department of Mathematics Central Michigan University Mt. Pleasant, MI 48859"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Central Michigan University Mt. Pleasant, MI 48859","institution_ids":["https://openalex.org/I1629065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017595199","display_name":"Douglas B. West","orcid":"https://orcid.org/0000-0001-8818-1667"},"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":"Douglas B. West","raw_affiliation_strings":["Department of Mathematics University of Illinois 1409 W. Green St. Urbana, IL 61801-2975"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Illinois 1409 W. Green St. Urbana, IL 61801-2975","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.17691195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"9","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.9986000061035156,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9965999722480774,"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":0.8866920471191406},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8146255016326904},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7668068408966064},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5997124910354614},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.592846155166626},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5556596517562866},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48626697063446045},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48486098647117615},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.46988868713378906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.056434303522109985}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8866920471191406},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8146255016326904},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7668068408966064},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5997124910354614},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.592846155166626},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5556596517562866},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48626697063446045},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48486098647117615},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.46988868713378906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.056434303522109985},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1665","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1665","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1n4/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":false,"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:10.1.1.89.3802","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.3802","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~west/pubs/2path.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1665","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1665","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1n4/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":false,"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/W2108615664.pdf","grobid_xml":"https://content.openalex.org/works/W2108615664.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1504855246","https://openalex.org/W2001568091","https://openalex.org/W2004308928","https://openalex.org/W2043506310"],"related_works":["https://openalex.org/W2058834578","https://openalex.org/W55187247","https://openalex.org/W1891636518","https://openalex.org/W264408731","https://openalex.org/W2073363580","https://openalex.org/W411819533","https://openalex.org/W2067430117","https://openalex.org/W4247056703","https://openalex.org/W2004734763","https://openalex.org/W1972516737"],"abstract_inverted_index":{"Let":[0],"$G$":[1,37],"be":[2],"a":[3,20,39],"connected":[4],"graph":[5],"that":[6,36],"is":[7],"the":[8],"edge-disjoint":[9],"union":[10],"of":[11,14,22,26,31,42],"two":[12],"paths":[13],"length":[15,43],"$n$,":[16],"where":[17],"$n\\ge2$.":[18],"Using":[19],"result":[21],"Thomason":[23],"on":[24],"decompositions":[25],"4-regular":[27],"graphs":[28],"into":[29],"pairs":[30],"Hamiltonian":[32],"cycles,":[33],"we":[34],"prove":[35],"has":[38],"third":[40],"path":[41],"$n$.":[44]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}