{"id":"https://openalex.org/W4407402586","doi":"https://doi.org/10.3103/s0146411624700470","title":"NP-Completeness of the Eulerian Walk Problem for a Multiple Graph","display_name":"NP-Completeness of the Eulerian Walk Problem for a Multiple Graph","publication_year":2024,"publication_date":"2024-12-01","ids":{"openalex":"https://openalex.org/W4407402586","doi":"https://doi.org/10.3103/s0146411624700470"},"language":"en","primary_location":{"id":"doi:10.3103/s0146411624700470","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411624700470","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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/A5019524013","display_name":"\u0410. \u0412. \u0421\u043c\u0438\u0440\u043d\u043e\u0432","orcid":"https://orcid.org/0000-0002-0980-2507"},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. V. Smirnov","raw_affiliation_strings":["Demidov Yaroslavl State University, 150003, Yaroslavl, Russia"],"raw_orcid":"https://orcid.org/0000-0002-0980-2507","affiliations":[{"raw_affiliation_string":"Demidov Yaroslavl State University, 150003, Yaroslavl, Russia","institution_ids":["https://openalex.org/I198371094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019524013"],"corresponding_institution_ids":["https://openalex.org/I198371094"],"apc_list":null,"apc_paid":null,"fwci":0.3457,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.67432034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"58","issue":"7","first_page":"1082","last_page":"1091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9961000084877014,"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/computer-science","display_name":"Computer science","score":0.7900173664093018},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.6895222663879395},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5949022769927979},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5916488170623779},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4612758159637451},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19298261404037476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.07201990485191345}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7900173664093018},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.6895222663879395},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5949022769927979},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5916488170623779},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4612758159637451},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19298261404037476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.07201990485191345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3103/s0146411624700470","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411624700470","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W100926944","https://openalex.org/W1586183010","https://openalex.org/W1973343935","https://openalex.org/W2041884875","https://openalex.org/W2048459753","https://openalex.org/W2314502764","https://openalex.org/W2540385142","https://openalex.org/W2572716357","https://openalex.org/W2922839089","https://openalex.org/W4293017958"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4366835705","https://openalex.org/W2034363746","https://openalex.org/W4399505169","https://openalex.org/W2008097580","https://openalex.org/W4237277701","https://openalex.org/W2930989993","https://openalex.org/W4308900515"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,152],"consider":[4],"undirected":[5],"multiple":[6,16,25,65,74,124,143],"graphs":[7],"of":[8,20,31,39,84,88,98,108,115,141,156,160],"any":[9],"natural":[10],"multiplicity":[11],"k":[12,85],">":[13],"1.":[14],"A":[15],"graph":[17],"contains":[18],"edges":[19,41,53,87],"three":[21],"types:":[22],"ordinary":[23,133,169],"edges,":[24,26,75],"and":[27,76],"multiedges.":[28],"Each":[29],"edge":[30],"the":[32,37,81,95,105,113,116,128,138,142,157,164],"last":[33],"two":[34],"types":[35],"is":[36,61,94,147],"union":[38],"linked":[40,52,86],"that":[42,137],"connect":[43],"2":[44],"or":[45,120],"(k":[46],"+":[47],"1)":[48],"vertices,":[49],"correspondingly.":[50],"The":[51],"should":[54],"be":[55,70,80,104],"used":[56],"simultaneously.":[57],"If":[58,91],"a":[59,64,89,92,99,123],"vertex":[60,93],"incident":[62,71],"to":[63,72],"edge,":[66],"then":[67,101],"it":[68,77,102],"can":[69,78],"other":[73],"also":[79],"common":[82,96,106],"end":[83,97,107],"multiedge.":[90,110],"multiedge,":[100],"cannot":[103],"another":[109],"We":[111,135],"study":[112],"problem":[114,130,146,159],"Eulerian":[117,144],"walk":[118,145],"(cycle":[119],"trail)":[121],"in":[122,167],"graph,":[125],"which":[126],"generalizes":[127],"classical":[129],"for":[131],"an":[132,168],"graph.":[134,170],"prove":[136,154],"recognition":[139],"variant":[140],"NP-complete.":[148],"To":[149],"do":[150],"this,":[151],"first":[153],"NP-completeness":[155],"auxiliary":[158],"covering":[161],"trails":[162],"with":[163],"given":[165],"endpoints":[166]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-01-24T23:23:39.755997","created_date":"2025-10-10T00:00:00"}