{"id":"https://openalex.org/W1802444145","doi":"https://doi.org/10.37236/2698","title":"Product Dimension of Forests and Bounded Treewidth Graphs","display_name":"Product Dimension of Forests and Bounded Treewidth Graphs","publication_year":2013,"publication_date":"2013-09-20","ids":{"openalex":"https://openalex.org/W1802444145","doi":"https://doi.org/10.37236/2698","mag":"1802444145"},"language":"en","primary_location":{"id":"doi:10.37236/2698","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2698","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i3p42/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i3p42/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024359075","display_name":"L. Sunil Chandran","orcid":"https://orcid.org/0000-0001-5451-6975"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"L. Sunil Chandran","raw_affiliation_strings":["Indian Institute of Science, Bangalore, India","Indian Inst. of Science, Bangalore  India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]},{"raw_affiliation_string":"Indian Inst. of Science, Bangalore  India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076736694","display_name":"Rogers Mathew","orcid":"https://orcid.org/0000-0003-4536-1136"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Rogers Mathew","raw_affiliation_strings":["Dalhousie University, Halifax, Canada","Dalhousie University, Halifax. Canada"],"affiliations":[{"raw_affiliation_string":"Dalhousie University, Halifax, Canada","institution_ids":["https://openalex.org/I129902397"]},{"raw_affiliation_string":"Dalhousie University, Halifax. Canada","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001903817","display_name":"Deepak Rajendraprasad","orcid":"https://orcid.org/0000-0001-9101-8967"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Deepak Rajendraprasad","raw_affiliation_strings":["Indian Institute of Science, Bangalore, India","Indian Inst. of Science, Bangalore  India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]},{"raw_affiliation_string":"Indian Inst. of Science, Bangalore  India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042086477","display_name":"Roohani Sharma","orcid":"https://orcid.org/0000-0003-2212-1359"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Roohani Sharma","raw_affiliation_strings":["Indian Institute of Science, Bangalore, India","Indian Inst. of Science, Bangalore  India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]},{"raw_affiliation_string":"Indian Inst. of Science, Bangalore  India","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024359075"],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04963619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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":0.8516359329223633},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.8358349204063416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.722309947013855},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6320676803588867},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.508979320526123},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48456302285194397},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.473217636346817},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4592973291873932},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4328494071960449},{"id":"https://openalex.org/keywords/partial-k-tree","display_name":"Partial k-tree","score":0.42285510897636414},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3130277395248413},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.27096959948539734},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.24463799595832825},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13700270652770996},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.046268314123153687}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8516359329223633},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8358349204063416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.722309947013855},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6320676803588867},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.508979320526123},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48456302285194397},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.473217636346817},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4592973291873932},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4328494071960449},{"id":"https://openalex.org/C128764233","wikidata":"https://www.wikidata.org/wiki/Q7140374","display_name":"Partial k-tree","level":5,"score":0.42285510897636414},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3130277395248413},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.27096959948539734},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.24463799595832825},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13700270652770996},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.046268314123153687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/2698","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2698","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i3p42/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"},{"id":"pmh:oai:arXiv.org:1209.2218","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.2218","pdf_url":"https://arxiv.org/pdf/1209.2218","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1802444145","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1209.2218v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1209.2218","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1209.2218","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/2698","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2698","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i3p42/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":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.7400000095367432}],"awards":[{"id":"https://openalex.org/G3631313543","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320308943","funder_display_name":"Microsoft Research"}],"funders":[{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1802444145.pdf","grobid_xml":"https://content.openalex.org/works/W1802444145.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W418761075","https://openalex.org/W1504202960","https://openalex.org/W1966657769","https://openalex.org/W1983193381","https://openalex.org/W1994281890","https://openalex.org/W2034198559","https://openalex.org/W2046157820","https://openalex.org/W2048790237","https://openalex.org/W2056930168","https://openalex.org/W2113835179","https://openalex.org/W2151120603","https://openalex.org/W2159421009","https://openalex.org/W2320377306","https://openalex.org/W2599861671","https://openalex.org/W2733114624","https://openalex.org/W6683678616"],"related_works":["https://openalex.org/W2105749797","https://openalex.org/W3197941146","https://openalex.org/W2952246555","https://openalex.org/W2945078344","https://openalex.org/W3100879432","https://openalex.org/W2790333339","https://openalex.org/W2953093257","https://openalex.org/W2561942106","https://openalex.org/W2558490395","https://openalex.org/W2185696233","https://openalex.org/W2765383521","https://openalex.org/W3128800975","https://openalex.org/W2958527737","https://openalex.org/W3016377020","https://openalex.org/W2294714952","https://openalex.org/W3137124880","https://openalex.org/W3014362497","https://openalex.org/W1978969142","https://openalex.org/W3092286751","https://openalex.org/W2526173822"],"abstract_inverted_index":{"The":[0,83],"product":[1,25,36,55,121,140],"dimension":[2,37,56,122,141],"of":[3,22,26,38,71,103,157],"a":[4,23,97],"graph":[5,111,135],"$G$":[6,17],"is":[7,18,92],"defined":[8],"as":[9],"the":[10,35,66,76,89,101,154,163],"minimum":[11],"natural":[12],"number":[13],"$l$":[14,27],"such":[15],"that":[16,48,109,132],"an":[19],"induced":[20],"subgraph":[21],"direct":[24],"complete":[28],"graphs.":[29,45],"In":[30],"this":[31],"paper":[32],"we":[33],"study":[34],"forests,":[39],"bounded":[40],"treewidth":[41,116],"graphs":[42],"and":[43,81,94,167],"$k$-degenerate":[44,134],"We":[46,129],"show":[47,108,131],"every":[49,110,133],"forest":[50],"on":[51,100,112,136],"$n$":[52,113,137],"vertices":[53,114,138],"has":[54,120,139],"at":[57,88,117,123,142],"most":[58,118,124,143],"$1.441":[59],"\\log":[60,73,147,160],"n":[61,126,148],"+":[62,127,150],"3$.":[63],"This":[64,152],"improves":[65,153],"best":[67],"known":[68],"upper":[69,155],"bound":[70,91,156],"$3":[72],"n$":[74,161],"for":[75,162],"same":[77,164],"due":[78],"to":[79,107],"Poljak":[80],"Pultr.":[82],"technique":[84],"used":[85],"in":[86],"arriving":[87],"above":[90],"extended":[93],"combined":[95],"with":[96,115],"well-known":[98],"result":[99],"existence":[102],"orthogonal":[104],"Latin":[105],"squares":[106],"$t$":[119],"$(t+2)(\\log":[125],"1)$.":[128],"also":[130],"$\\lceil":[144],"5.545":[145],"k":[146,159],"\\rceil":[149],"1$.":[151],"$32":[158],"by":[165],"Eaton":[166],"R\u0151dl.":[168]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
