{"id":"https://openalex.org/W4415428023","doi":"https://doi.org/10.3233/faia251259","title":"EFX Orientations of Multigraphs","display_name":"EFX Orientations of Multigraphs","publication_year":2025,"publication_date":"2025-10-21","ids":{"openalex":"https://openalex.org/W4415428023","doi":"https://doi.org/10.3233/faia251259"},"language":null,"primary_location":{"id":"doi:10.3233/faia251259","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia251259","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.3233/faia251259","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090532605","display_name":"Kevin Hsu","orcid":"https://orcid.org/0000-0002-8932-978X"},"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":true,"raw_author_name":"Kevin Hsu","raw_affiliation_strings":["University of Victoria"],"raw_orcid":"https://orcid.org/0000-0002-8932-978X","affiliations":[{"raw_affiliation_string":"University of Victoria","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090532605"],"corresponding_institution_ids":["https://openalex.org/I212119943"],"apc_list":null,"apc_paid":null,"fwci":5.4794,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.96533054,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":null,"issue":null,"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":0.6158999800682068,"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":0.6158999800682068,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.5906999707221985,"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"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.5638999938964844,"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/multigraph","display_name":"Multigraph","score":0.8378000259399414},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6305000185966492},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6241000294685364},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.4805000126361847},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4316999912261963}],"concepts":[{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.8378000259399414},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6305000185966492},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6241000294685364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6227999925613403},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6179999709129333},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.4805000126361847},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.24699999392032623}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/faia251259","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia251259","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.3233/faia251259","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia251259","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,34],"study":[1],"EFX":[2,80,99,143,154],"orientations":[3,155],"of":[4,56,69,78,91],"multigraphs":[5,146],"with":[6,66],"self-loops.":[7],"In":[8,64],"this":[9],"setting,":[10],"vertices":[11],"represent":[12,15],"agents,":[13,51],"edges":[14,53],"goods,":[16],"and":[17,52,111,145],"a":[18,87,114,117,128],"good":[19],"provides":[20],"positive":[21],"utility":[22,47],"to":[23,31,48,141],"an":[24,79,98],"agent":[25],"only":[26],"if":[27,104],"it":[28],"is":[29,101,106],"incident":[30,50],"the":[32,37,67,76,132],"agent.":[33],"focus":[35],"on":[36],"bi-valued":[38],"symmetric":[39,88],"case":[40,68],"in":[41,131,160],"which":[42,73],"each":[43],"edge":[44],"has":[45,97],"equal":[46],"both":[49],"have":[54,142,153],"one":[55],"two":[57],"possible":[58],"utilities":[59],"\u03b1":[60,108],">":[61,109],"\u03b2":[62],"\u22650.":[63],"contrast":[65],"simple":[70,137],"graphs":[71],"for":[72],"bipartiteness":[74],"implies":[75],"existence":[77],"orientation,":[81],"we":[82,123],"show":[83,124],"that":[84,125,134,147,156],"deciding":[85],"whether":[86],"multigraph":[89],"G":[90,105,112],"any":[92],"multiplicity":[93],"q":[94],"\u2265":[95],"2":[96],"orientation":[100],"NP-complete":[102],"even":[103,135],"bipartite,":[107],"q\u03b2,":[110],"contains":[113],"structure":[115,130],"called":[116],"non-trivial":[118],"odd":[119],"multitree":[120],"(NTOM).":[121],"Moreover,":[122],"NTOMs":[126,138,151],"are":[127],"problematic":[129],"sense":[133],"very":[136],"can":[139,157],"fail":[140],"orientations,":[144],"do":[148],"not":[149],"contain":[150],"always":[152],"be":[158],"found":[159],"polynomial-time.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-24T00:00:00"}