{"id":"https://openalex.org/W2035944364","doi":"https://doi.org/10.1002/(sici)1097-0118(200002)33:2<83::aid-jgt3>3.0.co;2-p","title":"Four-terminal reducibility and projective-planar wye-delta-wye-reducible graphs","display_name":"Four-terminal reducibility and projective-planar wye-delta-wye-reducible graphs","publication_year":2000,"publication_date":"2000-02-01","ids":{"openalex":"https://openalex.org/W2035944364","doi":"https://doi.org/10.1002/(sici)1097-0118(200002)33:2<83::aid-jgt3>3.0.co;2-p","mag":"2035944364"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(200002)33:2<83::aid-jgt3>3.0.co;2-p","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(200002)33:2<83::aid-jgt3>3.0.co;2-p","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5061516469","display_name":"Dan Archdeacon","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":"Dan Archdeacon","raw_affiliation_strings":["Dept. of Math. and Stat., University of Vermont, Burlington, VT 05405","Dept. of Math. and Stat., University of Vermont, Burlington, VT 05405#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Math. and Stat., University of Vermont, Burlington, VT 05405","institution_ids":["https://openalex.org/I111236770"]},{"raw_affiliation_string":"Dept. of Math. and Stat., University of Vermont, Burlington, VT 05405#TAB#","institution_ids":["https://openalex.org/I111236770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038008468","display_name":"Charles J. Colbourn","orcid":"https://orcid.org/0000-0002-3104-9515"},"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":"Charles J. Colbourn","raw_affiliation_strings":["Dept. of Computer Science, University of Vermont, Burlington, VT 05405","Department of Computer Science, University of Vermont, Burlington, VT 05405"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, University of Vermont, Burlington, VT 05405","institution_ids":["https://openalex.org/I111236770"]},{"raw_affiliation_string":"Department of Computer Science, University of Vermont, Burlington, VT 05405","institution_ids":["https://openalex.org/I111236770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068183979","display_name":"Isidoro Gitler","orcid":"https://orcid.org/0000-0003-1241-5943"},"institutions":[{"id":"https://openalex.org/I59361560","display_name":"Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/059sp8j34","country_code":"MX","type":"education","lineage":["https://openalex.org/I59361560"]},{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Isidoro Gitler","raw_affiliation_strings":["Departamento de Matema\u0301ticas, Centro de Investigacio\u0301n, y Estudios Avanzados del IPN, Apartado Postal 14-740, Me\u0301xico, D.F. 07000 Mexico","Departamento de Matem\u00e1ticas, Centro de Investigaci\u00f3n, y Estudios Avanzados del IPN, Apartado Postal 14-740, M\u00e9xico, D.F. 07000 Mexico#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matema\u0301ticas, Centro de Investigacio\u0301n, y Estudios Avanzados del IPN, Apartado Postal 14-740, Me\u0301xico, D.F. 07000 Mexico","institution_ids":["https://openalex.org/I59361560","https://openalex.org/I68368234"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Centro de Investigaci\u00f3n, y Estudios Avanzados del IPN, Apartado Postal 14-740, M\u00e9xico, D.F. 07000 Mexico#TAB#","institution_ids":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005781105","display_name":"J. Scott Provan","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Scott Provan","raw_affiliation_strings":["Operations Research, University of North Carolina, Chapel Hill, NC 27599","Operations Research, University of North Carolina, Chapel Hill, NC 27599#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Operations Research, University of North Carolina, Chapel Hill, NC 27599","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Operations Research, University of North Carolina, Chapel Hill, NC 27599#TAB#","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005781105","https://openalex.org/A5038008468","https://openalex.org/A5061516469","https://openalex.org/A5068183979"],"corresponding_institution_ids":["https://openalex.org/I111236770","https://openalex.org/I114027177","https://openalex.org/I59361560","https://openalex.org/I68368234"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.409,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.81714244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"2","first_page":"83","last_page":"93"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9958999752998352,"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/T11567","display_name":"semigroups and automata theory","score":0.9929999709129333,"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/combinatorics","display_name":"Combinatorics","score":0.8461304903030396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7251369953155518},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6823854446411133},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.520105242729187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44127020239830017},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4233993589878082},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4106895923614502},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.30412986874580383}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8461304903030396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7251369953155518},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6823854446411133},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.520105242729187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44127020239830017},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4233993589878082},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4106895923614502},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.30412986874580383}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/(sici)1097-0118(200002)33:2<83::aid-jgt3>3.0.co;2-p","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(200002)33:2<83::aid-jgt3>3.0.co;2-p","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.4988","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4988","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emba.uvm.edu/~archdeac/papers/deltawye.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.5507","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.5507","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emba.uvm.edu/~colbourn/src/4term.ps","raw_type":"text"},{"id":"mag:2035944364","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W131078572","https://openalex.org/W1969229778","https://openalex.org/W1972872923","https://openalex.org/W1989650529","https://openalex.org/W1995138470","https://openalex.org/W1997601296","https://openalex.org/W2012682075","https://openalex.org/W2013844317","https://openalex.org/W2031769269","https://openalex.org/W2043915914","https://openalex.org/W2051077495","https://openalex.org/W2071605752","https://openalex.org/W2081589084","https://openalex.org/W2090034967","https://openalex.org/W2117889403","https://openalex.org/W2133388875","https://openalex.org/W2324792688","https://openalex.org/W2330548796","https://openalex.org/W2520463769"],"related_works":["https://openalex.org/W2133388875","https://openalex.org/W2520463769","https://openalex.org/W2324792688","https://openalex.org/W2031769269","https://openalex.org/W2999620721","https://openalex.org/W2122610181","https://openalex.org/W565024699","https://openalex.org/W2964332702","https://openalex.org/W2793674553","https://openalex.org/W2141665721","https://openalex.org/W2125924733","https://openalex.org/W2078498425","https://openalex.org/W1995138470","https://openalex.org/W1977702434","https://openalex.org/W1969229778","https://openalex.org/W1514441594","https://openalex.org/W1576388809","https://openalex.org/W2086172547","https://openalex.org/W2018894613","https://openalex.org/W1902280874"],"abstract_inverted_index":{"A":[0],"graph":[1],"is":[2],"Y\u0394Y-reducible":[3,42,60],"if":[4],"it":[5],"can":[6],"be":[7,26],"reduced":[8],"to":[9],"a":[10,13],"vertex":[11],"by":[12,28],"sequence":[14],"of":[15,47,74],"series-parallel":[16],"reductions":[17,29],"and":[18,30,70],"Y\u0394Y-transformations.":[19],"Terminals":[20],"are":[21,41,77],"distinguished":[22],"vertices,":[23],"that":[24,37,72],"cannot":[25],"deleted":[27],"transformations.":[31],"In":[32],"this":[33,56],"article,":[34],"we":[35,58],"show":[36],"four-terminal":[38],"planar":[39],"graphs":[40,73],"when":[43],"at":[44],"least":[45],"three":[46],"the":[48,52],"vertices":[49],"lie":[50],"on":[51],"same":[53],"face.":[54],"Using":[55],"result,":[57],"characterize":[59],"projective-planar":[61,68],"graphs.":[62],"We":[63],"also":[64],"consider":[65],"terminals":[66],"in":[67],"graphs,":[69],"establish":[71],"crossing-number":[75],"one":[76],"Y\u0394Y-reducible.":[78],"\u00a9":[79],"2000":[80,91],"John":[81],"Wiley":[82],"&":[83],"Sons,":[84],"Inc.":[85],"J":[86],"Graph":[87],"Theory":[88],"33:":[89],"83\u201393,":[90]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}
