{"id":"https://openalex.org/W1746068744","doi":"https://doi.org/10.37236/1199","title":"The Prism of the Acyclic Orientation Graph is Hamiltonian","display_name":"The Prism of the Acyclic Orientation Graph is Hamiltonian","publication_year":1995,"publication_date":"1995-03-13","ids":{"openalex":"https://openalex.org/W1746068744","doi":"https://doi.org/10.37236/1199","mag":"1746068744"},"language":"en","primary_location":{"id":"doi:10.37236/1199","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1199","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r5/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/v2i1r5/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053341628","display_name":"Gara Pruesse","orcid":null},"institutions":[{"id":"https://openalex.org/I111236770","display_name":"University of Vermont","ror":"https://ror.org/0155zta11","country_code":"US","type":"education","lineage":["https://openalex.org/I111236770"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gara Pruesse","raw_affiliation_strings":["UNIVERSITY OF VERMONT"],"affiliations":[{"raw_affiliation_string":"UNIVERSITY OF VERMONT","institution_ids":["https://openalex.org/I111236770"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048017151","display_name":"Frank Ruskey","orcid":"https://orcid.org/0000-0001-5523-7185"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Frank Ruskey","raw_affiliation_strings":["University of Victoria"],"affiliations":[{"raw_affiliation_string":"University of Victoria","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053341628"],"corresponding_institution_ids":["https://openalex.org/I111236770"],"apc_list":null,"apc_paid":null,"fwci":2.1406,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85538816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","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":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9986000061035156,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9902999997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7222443222999573},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7074445486068726},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5909578800201416},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5518956780433655},{"id":"https://openalex.org/keywords/quartic-graph","display_name":"Quartic graph","score":0.4666590392589569},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.4556863307952881},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.4476388096809387},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.41388171911239624},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.41103655099868774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38213425874710083},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3611519932746887},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3051201403141022}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7222443222999573},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7074445486068726},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5909578800201416},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5518956780433655},{"id":"https://openalex.org/C199692417","wikidata":"https://www.wikidata.org/wiki/Q7269362","display_name":"Quartic graph","level":5,"score":0.4666590392589569},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.4556863307952881},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.4476388096809387},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.41388171911239624},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.41103655099868774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38213425874710083},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3611519932746887},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3051201403141022},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1199","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1199","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r5/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:10.1.1.47.6847","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.6847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.zblmath.fiz-karlsruhe.de/e-journals/EJC/Volume_2/../Volume_2/PostScriptfiles/v2i1r5.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.9116","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.9116","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://csr.csc.uvic.ca/home/fruskey/Publications/PrismOrient.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.8177","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.8177","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_2/PDF/v2i1r5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1199","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1199","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r5/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":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8635741758","display_name":"VERMONT EPSCoR SYSTEMIC IMPROVEMENT PLAN","funder_award_id":"9350540","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1746068744.pdf","grobid_xml":"https://content.openalex.org/works/W1746068744.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W156470527","https://openalex.org/W1993776407","https://openalex.org/W2056239531"],"related_works":["https://openalex.org/W2377278407","https://openalex.org/W1534832295","https://openalex.org/W2057580655","https://openalex.org/W1978219832","https://openalex.org/W2040301912","https://openalex.org/W2118680612","https://openalex.org/W2080073042","https://openalex.org/W2278094798","https://openalex.org/W2319833372","https://openalex.org/W2070086094"],"abstract_inverted_index":{"Every":[0],"connected":[1,43,96],"simple":[2],"graph":[3,11,76,92],"$G$":[4,20,72],"has":[5],"an":[6],"acyclic":[7,17],"orientation.":[8],"Define":[9],"a":[10,33,74],"${AO}(G)$":[12,41,85,93],"whose":[13,22],"vertices":[14],"are":[15],"the":[16,30,52,59,64,103],"orientations":[18,25],"of":[19,32],"and":[21],"edges":[23,78],"join":[24],"that":[26,40,51,63,102],"differ":[27],"by":[28],"reversing":[29],"direction":[31],"single":[34],"edge.":[35],"It":[36],"was":[37],"known":[38],"previously":[39],"is":[42,55,69,73,94,105],"but":[44,80,97],"not":[45,81,106],"necessarily":[46,82,107],"Hamiltonian.":[47,56,70,108],"However,":[48],"Squire":[49],"proved":[50],"square":[53],"${AO}(G)^2$":[54],"We":[57],"prove":[58],"slightly":[60],"stronger":[61],"result":[62],"prism":[65,104],"${AO}(G)":[66],"\\times":[67],"e$":[68],"If":[71],"mixed":[75],"(some":[77],"directed,":[79],"all),":[83],"then":[84],"can":[86],"be":[87],"defined":[88],"as":[89],"before.":[90],"The":[91],"again":[95],"we":[98],"give":[99],"examples":[100],"showing":[101]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
