{"id":"https://openalex.org/W2062429212","doi":"https://doi.org/10.1002/net.3230220704","title":"Counting <i>k</i>\u2010component forests of a graph","display_name":"Counting <i>k</i>\u2010component forests of a graph","publication_year":1992,"publication_date":"1992-12-01","ids":{"openalex":"https://openalex.org/W2062429212","doi":"https://doi.org/10.1002/net.3230220704","mag":"2062429212"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230220704","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230220704","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"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":"Networks","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/A5037417281","display_name":"Wendy Myrvold","orcid":"https://orcid.org/0000-0002-0401-013X"},"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":"Wendy Myrvold","raw_affiliation_strings":["Department of Computer Science University of Victoria P.O. Box 3055 Victoria, B.C. V8W 3P6, Canada","Department of Computer Science, University of Victoria, P.O. Box 3055, Victoria, B.C., V8W 3P6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Victoria P.O. Box 3055 Victoria, B.C. V8W 3P6, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Computer Science, University of Victoria, P.O. Box 3055, Victoria, B.C., V8W 3P6, Canada","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037417281"],"corresponding_institution_ids":["https://openalex.org/I212119943"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.20234674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"7","first_page":"647","last_page":"652"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987999796867371,"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/T11476","display_name":"Graph theory and applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7304964661598206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6917484998703003},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.623525083065033},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5727068781852722},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.552952766418457},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5359647274017334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5020015239715576},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.49164754152297974},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48612046241760254},{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.4847238063812256},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2607087790966034},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.21211537718772888}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7304964661598206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6917484998703003},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.623525083065033},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5727068781852722},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.552952766418457},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5359647274017334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5020015239715576},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.49164754152297974},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48612046241760254},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.4847238063812256},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2607087790966034},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.21211537718772888}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230220704","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230220704","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"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":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W322131040","https://openalex.org/W1484040084","https://openalex.org/W1574303240","https://openalex.org/W1655990431","https://openalex.org/W1971833343","https://openalex.org/W1974977713","https://openalex.org/W1979740015","https://openalex.org/W1987374783","https://openalex.org/W2032929335","https://openalex.org/W2035476608","https://openalex.org/W2080063509","https://openalex.org/W2101196233","https://openalex.org/W2117889403","https://openalex.org/W2314240464","https://openalex.org/W2596951540","https://openalex.org/W4232455638","https://openalex.org/W4252112222"],"related_works":["https://openalex.org/W2491866269","https://openalex.org/W2246199414","https://openalex.org/W4300508906","https://openalex.org/W40451570","https://openalex.org/W2408698893","https://openalex.org/W2150420791","https://openalex.org/W2949669097","https://openalex.org/W4289752603","https://openalex.org/W2080137701","https://openalex.org/W2202852987"],"abstract_inverted_index":{"Abstract":[0],"We":[1,111],"describe":[2],"an":[3,99],"algorithm":[4,28,100],"for":[5,23,101],"computing":[6],"the":[7,60,67,82,90,124],"number":[8,68,75,83],"of":[9,14,45,51,69,73,77,84,95,107,127],"k":[10,25],"\u2010component":[11],"spanning":[12,71,104],"forests":[13,88],"a":[15,41,49,78,108],"graph":[16,80],"G":[17],"that":[18],"runs":[19],"in":[20,89,117],"polynomial":[21],"time":[22,62,118,125],"fixed":[24],".":[26],"The":[27],"is":[29,98,123],"based":[30],"on":[31],"earlier":[32],"work":[33],"by":[34,132],"Liu":[35],"and":[36,48],"Chow.":[37],"Our":[38],"contributions":[39],"are":[40],"simpler":[42],"graph\u2010theoretic":[43],"proof":[44],"their":[46],"formula":[47],"demonstration":[50],"how":[52],"Jacobi's":[53],"Theorem":[54],"can":[55,114],"be":[56,115],"applied":[57],"to":[58],"improve":[59],"asymptotic":[61],"complexity.":[63],"By":[64],"matroid":[65],"duality,":[66],"connected":[70,103],"subgraphs":[72,106],"cyclomatic":[74],"c":[76,85],"planar":[79,109],"equals":[81],"+":[86],"1\u2010component":[87],"dual.":[91],"Thus,":[92],"one":[93],"application":[94],"this":[96,113],"research":[97],"counting":[102],"unicyclic":[105],"graph.":[110],"show":[112],"done":[116],"O(M(n))":[119],",":[120],"where":[121],"M(n)":[122],"complexity":[126],"multiplying":[128],"together":[129],"two":[130],"n":[131,133],"matrices.":[134]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}