{"id":"https://openalex.org/W2148443734","doi":"https://doi.org/10.37236/3826","title":"Maximum Induced Forests in Graphs of Bounded Treewidth","display_name":"Maximum Induced Forests in Graphs of Bounded Treewidth","publication_year":2013,"publication_date":"2013-10-28","ids":{"openalex":"https://openalex.org/W2148443734","doi":"https://doi.org/10.37236/3826","mag":"2148443734"},"language":"en","primary_location":{"id":"doi:10.37236/3826","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3826","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i4p8/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/v20i4p8/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046311408","display_name":"Glenn G. Chappell","orcid":null},"institutions":[{"id":"https://openalex.org/I2802090665","display_name":"University of Alaska System","ror":"https://ror.org/01mtkd993","country_code":"US","type":"education","lineage":["https://openalex.org/I2802090665"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Glenn G. Chappell","raw_affiliation_strings":["University of Alaska"],"affiliations":[{"raw_affiliation_string":"University of Alaska","institution_ids":["https://openalex.org/I2802090665"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068581962","display_name":"Michael J. Pelsmajer","orcid":"https://orcid.org/0000-0001-9688-5787"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael J. Pelsmajer","raw_affiliation_strings":["Illinois Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Illinois Institute of Technology","institution_ids":["https://openalex.org/I180949307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046311408"],"corresponding_institution_ids":["https://openalex.org/I2802090665"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.15460266,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"4","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":0.9984999895095825,"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":0.9984999895095825,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9854999780654907,"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"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9696000218391418,"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/treewidth","display_name":"Treewidth","score":0.9310665130615234},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8840250968933105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7831971645355225},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7112137079238892},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6750903129577637},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6009629964828491},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.579475462436676},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5659887790679932},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.360828161239624},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.16100463271141052},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.043105125427246094}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.9310665130615234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8840250968933105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7831971645355225},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7112137079238892},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6750903129577637},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6009629964828491},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.579475462436676},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5659887790679932},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.360828161239624},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.16100463271141052},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.043105125427246094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3826","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3826","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i4p8/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:10.37236/3826","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3826","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i4p8/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":[{"score":0.699999988079071,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2148443734.pdf"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W132145278","https://openalex.org/W273972581","https://openalex.org/W1480480697","https://openalex.org/W1871156538","https://openalex.org/W1977080610","https://openalex.org/W1980392837","https://openalex.org/W1984038535","https://openalex.org/W1999519812","https://openalex.org/W2000338110","https://openalex.org/W2025085400","https://openalex.org/W2028168192","https://openalex.org/W2032274094","https://openalex.org/W2087083200","https://openalex.org/W2089435810","https://openalex.org/W2513712380","https://openalex.org/W3170070061","https://openalex.org/W4213087285","https://openalex.org/W4242102268","https://openalex.org/W4245619149","https://openalex.org/W6669897299"],"related_works":["https://openalex.org/W2949617446","https://openalex.org/W4294299870","https://openalex.org/W2748664888","https://openalex.org/W1582492864","https://openalex.org/W35387897","https://openalex.org/W2745231626","https://openalex.org/W4299559467","https://openalex.org/W2964174631","https://openalex.org/W1810116456","https://openalex.org/W4300619607"],"abstract_inverted_index":{"Given":[0],"a":[1,6,53,83,114,137],"nonnegative":[2],"integer":[3],"$d$":[4],"and":[5,37,47,58,67,97,111,125],"graph":[7,54],"$G$,":[8],"let":[9],"$f_d(G)$":[10,32],"be":[11,92],"the":[12,35,107,122],"maximum":[13,22],"order":[14,36,56],"of":[15,39,143],"an":[16],"induced":[17],"forest":[18],"in":[19],"$G$":[20,51],"having":[21],"degree":[23],"at":[24,60],"most":[25,61],"$d$.":[26],"We":[27,69,119],"seek":[28],"lower":[29],"bounds":[30],"for":[31,43,85,101,134],"based":[33],"on":[34,136],"treewidth":[38,59],"$G$.We":[40],"show":[41,73],"that,":[42],"all":[44],"$k,d\\ge":[45],"2$":[46],"$n\\ge":[48],"1$,":[49],"if":[50],"is":[52,77],"with":[55],"$n$":[57],"$k$,":[62],"then":[63],"$f_d(G)\\ge\\lceil{(2dn+2)/(kd+d+1)}\\rceil$,":[64],"unless":[65],"$G\\in\\{K_{1,1,3},K_{2,3}\\}$":[66],"$k=d=2$.":[68],"give":[70],"examples":[71],"that":[72,74],"this":[75],"bound":[76,84],"tight":[78,93],"to":[79,94,132],"within":[80,95],"$1$.We":[81],"conjecture":[82,108],"$d=1$:":[86],"$f_1(G)":[87],"\\ge\\lceil{2n/(k+2)}\\rceil$,":[88],"which":[89],"would":[90],"also":[91,120],"$1$,":[96],"we":[98,112,127],"prove":[99,113],"it":[100],"$k\\le":[102],"3$.":[103],"For":[104],"$k\\ge":[105],"4$":[106],"remains":[109],"open,":[110],"weaker":[115],"bound:":[116],"$f_1(G)\\ge":[117],"(2n+2)/(2k+3)$.":[118],"examine":[121],"cases":[123],"$d=0$":[124],"$k=0,1$.Lastly,":[126],"consider":[128],"open":[129],"problems":[130],"relating":[131],"$f_d$":[133],"graphs":[135,142],"given":[138],"surface,":[139],"rather":[140],"than":[141],"bounded":[144],"treewidth.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}