{"id":"https://openalex.org/W1566691392","doi":"https://doi.org/10.37236/708","title":"Equitable Partitions to Spanning Trees in a Graph","display_name":"Equitable Partitions to Spanning Trees in a Graph","publication_year":2011,"publication_date":"2011-11-21","ids":{"openalex":"https://openalex.org/W1566691392","doi":"https://doi.org/10.37236/708","mag":"1566691392"},"language":"en","primary_location":{"id":"doi:10.37236/708","is_oa":true,"landing_page_url":"https://doi.org/10.37236/708","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p221/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p221/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100990699","display_name":"Zsolt Fekete","orcid":null},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Zsolt Fekete","raw_affiliation_strings":["Data Mining and Web search Research Group, Informatics Laboratory, Computer and Automation Research Institute, Hungarian Academy of Sciences","Hungarian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Mining and Web search Research Group, Informatics Laboratory, Computer and Automation Research Institute, Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I7597260"]},{"raw_affiliation_string":"Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109584874","display_name":"J\u00e1cint Szab\u00f3","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J\u00e1cint Szab\u00f3","raw_affiliation_strings":["IBM, ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM, ,","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3261,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.57344757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.98580002784729,"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"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9763000011444092,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8542468547821045},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.846328616142273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8238622546195984},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.5829193592071533},{"id":"https://openalex.org/keywords/connected-dominating-set","display_name":"Connected dominating set","score":0.5767875909805298},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.47786229848861694},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45513781905174255},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.447086364030838},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4357500374317169},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.43471789360046387},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4122750163078308},{"id":"https://openalex.org/keywords/tr\u00e9maux-tree","display_name":"Tr\u00e9maux tree","score":0.4110974967479706},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.1656450629234314},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13579300045967102}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8542468547821045},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.846328616142273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8238622546195984},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.5829193592071533},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.5767875909805298},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.47786229848861694},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45513781905174255},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.447086364030838},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4357500374317169},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.43471789360046387},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4122750163078308},{"id":"https://openalex.org/C124302570","wikidata":"https://www.wikidata.org/wiki/Q7849146","display_name":"Tr\u00e9maux tree","level":5,"score":0.4110974967479706},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.1656450629234314},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13579300045967102},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/708","is_oa":true,"landing_page_url":"https://doi.org/10.37236/708","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p221/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/708","is_oa":true,"landing_page_url":"https://doi.org/10.37236/708","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p221/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1566691392.pdf","grobid_xml":"https://content.openalex.org/works/W1566691392.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2009551324","https://openalex.org/W2010042187","https://openalex.org/W2087816994","https://openalex.org/W2340149117","https://openalex.org/W2988480584","https://openalex.org/W4251345737"],"related_works":["https://openalex.org/W2911818503","https://openalex.org/W4231397933","https://openalex.org/W2307044859","https://openalex.org/W4380840098","https://openalex.org/W2014991506","https://openalex.org/W2779618893","https://openalex.org/W2138987445","https://openalex.org/W1738503018","https://openalex.org/W2069643240","https://openalex.org/W3195481350"],"abstract_inverted_index":{"In":[0],"this":[1,57],"paper":[2,51],"we":[3],"first":[4],"prove":[5],"that":[6,38,93],"if":[7],"the":[8,16,50,60,67,95],"edge":[9,61],"set":[10,62,80],"of":[11,19,21,30,49,56,63,70,72,81,83,97,110],"an":[12],"undirected":[13],"graph":[14,65],"is":[15,52,66],"disjoint":[17,68],"union":[18,69],"two":[20,42,71],"its":[22,73],"spanning":[23,35,74,90],"trees,":[24,75],"then":[25,76],"for":[26,77,107],"every":[27,78],"subset":[28],"$P$":[29,40],"edges":[31],"there":[32,86],"exists":[33,87],"a":[34,53,64,89],"tree":[36,91],"decomposition":[37,92],"cuts":[39,94],"into":[41,100],"(almost)":[43,101],"equal":[44,102],"parts.":[45,103],"The":[46,112],"main":[47],"result":[48,105],"further":[54],"extension":[55],"claim:":[58],"If":[59],"stable":[79],"vertices":[82,99],"size":[84],"3,":[85],"such":[88],"stars":[96],"these":[98],"This":[104],"fails":[106],"4":[108],"instead":[109],"3.":[111],"proofs":[113],"are":[114],"elementary.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
