{"id":"https://openalex.org/W2038219335","doi":"https://doi.org/10.1137/s0895480192238172","title":"Dual Eulerian Properties of Plane Multigraphs","display_name":"Dual Eulerian Properties of Plane Multigraphs","publication_year":1995,"publication_date":"1995-02-01","ids":{"openalex":"https://openalex.org/W2038219335","doi":"https://doi.org/10.1137/s0895480192238172","mag":"2038219335"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480192238172","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480192238172","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5019287169","display_name":"B.S. Carlson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bradley S. Carlson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037428632","display_name":"C. Y. Roger Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Y. Roger Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029481594","display_name":"Dikran S. Meliksetian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dikran S. Meliksetian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5214,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.7289823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"1","first_page":"33","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9951000213623047,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9951000213623047,"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"}},{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9889000058174133,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9758999943733215,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multigraph","display_name":"Multigraph","score":0.9862837791442871},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.9528524875640869},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6476101875305176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6459674835205078},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5570849180221558},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5277985334396362},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5058419704437256},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.48404449224472046},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47425973415374756},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4555247724056244},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36865493655204773},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26511168479919434},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.2142585813999176},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14416003227233887}],"concepts":[{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.9862837791442871},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.9528524875640869},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6476101875305176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6459674835205078},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5570849180221558},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5277985334396362},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5058419704437256},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.48404449224472046},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47425973415374756},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4555247724056244},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36865493655204773},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26511168479919434},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.2142585813999176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14416003227233887},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895480192238172","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480192238172","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dspace.sunyconnect.suny.edu:1951/37259","is_oa":false,"landing_page_url":"http://hdl.handle.net/1951/37259","pdf_url":null,"source":{"id":"https://openalex.org/S4306400078","display_name":"SUNY Digital Repository Support (State University of New York System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63190737","host_organization_name":"University at Buffalo, State University of New York","host_organization_lineage":["https://openalex.org/I63190737"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Technical Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1548521138","https://openalex.org/W1556279008","https://openalex.org/W1987067207","https://openalex.org/W2099412608","https://openalex.org/W2113320865","https://openalex.org/W2130250653","https://openalex.org/W2314885430"],"related_works":["https://openalex.org/W2553746213","https://openalex.org/W1788536844","https://openalex.org/W2248632506","https://openalex.org/W24573320","https://openalex.org/W1974848406","https://openalex.org/W11818456","https://openalex.org/W2137952152","https://openalex.org/W2073563998","https://openalex.org/W2038219335","https://openalex.org/W1763095158"],"abstract_inverted_index":{"A":[0],"plane":[1,35,47,77,93],"multigraph":[2,48,63,78,94],"is":[3,53,67,83,95,123],"said":[4],"to":[5,49,64,79,104,133],"be":[6,50,65,80,99,131],"dual":[7,14,51,81,96],"Eulerian":[8,52,66,82,97],"if":[9],"both":[10],"it":[11],"and":[12,21,39,42,58,72,116],"its":[13],"contain":[15],"an":[16,117],"Euler":[17,23],"path":[18],"or":[19,90],"circuit":[20],"the":[22,56,70,86,109,114,134],"paths":[24],"have":[25],"corresponding":[26],"edge":[27],"sequences.":[28],"In":[29],"this":[30,121,126],"paper":[31],"several":[32],"properties":[33],"of":[34,88,108,111,113,137],"multigraphs":[36],"are":[37],"derived,":[38],"a":[40,46,62,76,92,105],"necessary":[41,57,71],"sufficient":[43,59,73],"condition":[44,60,74],"for":[45,61,75,140],"given.":[54],"Although":[55],"somewhat":[68],"trivial,":[69],"not.":[84],"Nevertheless,":[85],"question":[87,122],"whether":[89],"not":[91],"can":[98,130],"answered":[100],"in":[101,125],"time":[102],"proportional":[103],"linear":[106],"function":[107],"number":[110],"edges":[112],"graph,":[115],"algorithm":[118],"that":[119],"answers":[120],"presented":[124],"paper.":[127],"This":[128],"theory":[129],"applied":[132],"layout":[135],"synthesis":[136],"functional":[138],"cells":[139],"Complementary":[141],"Metal-Oxide":[142],"Semiconductor":[143],"Very":[144],"Large-Scale":[145],"Integrated":[146],"circuits.":[147]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}