{"id":"https://openalex.org/W2089018301","doi":"https://doi.org/10.1002/(sici)1097-0037(199708)30:1<23::aid-net3>3.0.co;2-n","title":"Maximizing spanning trees in almost complete graphs","display_name":"Maximizing spanning trees in almost complete graphs","publication_year":1997,"publication_date":"1997-08-01","ids":{"openalex":"https://openalex.org/W2089018301","doi":"https://doi.org/10.1002/(sici)1097-0037(199708)30:1<23::aid-net3>3.0.co;2-n","mag":"2089018301"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0037(199708)30:1<23::aid-net3>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199708)30:1<23::aid-net3>3.0.co;2-n","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/A5019504125","display_name":"Bryan Gilbert","orcid":null},"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":false,"raw_author_name":"Bryan Gilbert","raw_affiliation_strings":["University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6","Department of Computer Science, University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6"],"affiliations":[{"raw_affiliation_string":"University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Computer Science, University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"last","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":["University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6","Department of Computer Science, University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6"],"affiliations":[{"raw_affiliation_string":"University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Computer Science, University of Victoria, P.O. Box 3055, MS 7209, Victoria, BC, Canada V8W 3P6","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":24,"citation_normalized_percentile":{"value":0.21918461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"30","issue":"1","first_page":"23","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"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":0.9988999962806702,"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":0.9975000023841858,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/spanning-tree","display_name":"Spanning tree","score":0.824479341506958},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7081185579299927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.657159686088562},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6421425938606262},{"id":"https://openalex.org/keywords/tr\u00e9maux-tree","display_name":"Tr\u00e9maux tree","score":0.5333713293075562},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5207490921020508},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.47211945056915283},{"id":"https://openalex.org/keywords/arboricity","display_name":"Arboricity","score":0.45432865619659424},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44173815846443176},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.427217960357666},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.4117436408996582},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4116094410419464},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.41074705123901367},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.29242753982543945},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.18537479639053345},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.09762150049209595}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.824479341506958},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7081185579299927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.657159686088562},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6421425938606262},{"id":"https://openalex.org/C124302570","wikidata":"https://www.wikidata.org/wiki/Q7849146","display_name":"Tr\u00e9maux tree","level":5,"score":0.5333713293075562},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5207490921020508},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.47211945056915283},{"id":"https://openalex.org/C83204008","wikidata":"https://www.wikidata.org/wiki/Q4784907","display_name":"Arboricity","level":4,"score":0.45432865619659424},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44173815846443176},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.427217960357666},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.4117436408996582},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4116094410419464},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.41074705123901367},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.29242753982543945},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.18537479639053345},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.09762150049209595},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0037(199708)30:1<23::aid-net3>3.0.co;2-n","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199708)30:1<23::aid-net3>3.0.co;2-n","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1966931974","https://openalex.org/W4231397933","https://openalex.org/W2911818503","https://openalex.org/W2307044859","https://openalex.org/W2041764189","https://openalex.org/W2374925474","https://openalex.org/W2779618893","https://openalex.org/W2014991506","https://openalex.org/W1738503018","https://openalex.org/W3195481350"],"abstract_inverted_index":{"We":[0,58],"examine":[1],"the":[2,24,49,55,73],"family":[3,77],"of":[4,11,26,38,41,51,82],"graphs":[5,74],"whose":[6],"complements":[7],"are":[8],"a":[9,17,35,39,79],"union":[10],"paths":[12],"and":[13,15],"cycles":[14],"develop":[16,68],"very":[18],"simple":[19,36],"algebraic":[20],"technique":[21],"for":[22,62],"comparing":[23],"number":[25,50,81],"spanning":[27,52,83],"trees.":[28,84],"With":[29],"our":[30],"algebra,":[31],"we":[32,67],"can":[33],"obtain":[34],"proof":[37],"result":[40],"Kel'mans":[42],"that":[43,66],"evening":[44],"out":[45],"path":[46],"lengths":[47],"increases":[48],"trees":[53],"in":[54,75],"complement":[56],"graph.":[57],"provide":[59],"similar":[60],"characterizations":[61],"cycles.":[63],"The":[64],"theorems":[65],"enable":[69],"us":[70],"to":[71],"characterize":[72],"this":[76],"with":[78],"maximum":[80],"\u00a9":[85],"1997":[86,94],"John":[87],"Wiley":[88],"&":[89],"Sons,":[90],"Inc.":[91],"Networks":[92],"30:23\u201330,":[93]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}