{"id":"https://openalex.org/W1570869955","doi":"https://doi.org/10.37236/595","title":"On $(\\delta, \\chi)$-Bounded Families of Graphs","display_name":"On $(\\delta, \\chi)$-Bounded Families of Graphs","publication_year":2011,"publication_date":"2011-05-08","ids":{"openalex":"https://openalex.org/W1570869955","doi":"https://doi.org/10.37236/595","mag":"1570869955"},"language":"en","primary_location":{"id":"doi:10.37236/595","is_oa":true,"landing_page_url":"https://doi.org/10.37236/595","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p108/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/v18i1p108/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020847160","display_name":"Andr\u00e1s Gy\u00e1rf\u00e1s","orcid":"https://orcid.org/0000-0001-6173-1008"},"institutions":[{"id":"https://openalex.org/I161028277","display_name":"Institute for Advanced Studies in Basic Sciences","ror":"https://ror.org/00bzsst90","country_code":"IR","type":"education","lineage":["https://openalex.org/I161028277"]},{"id":"https://openalex.org/I4210117195","display_name":"HUN-REN Institute for Computer Science and Control","ror":"https://ror.org/0249v7n71","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210117195","https://openalex.org/I4387152226"]},{"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","IR"],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Gy\u00e1rf\u00e1s","raw_affiliation_strings":["Department of Mathematics,","Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran","Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, P.O. Box 63 Budapest, Hungary, H-1518"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics,","institution_ids":[]},{"raw_affiliation_string":"Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran","institution_ids":["https://openalex.org/I161028277"]},{"raw_affiliation_string":"Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, P.O. Box 63 Budapest, Hungary, H-1518","institution_ids":["https://openalex.org/I7597260","https://openalex.org/I4210117195"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012008426","display_name":"Manouchehr Zaker","orcid":null},"institutions":[{"id":"https://openalex.org/I161028277","display_name":"Institute for Advanced Studies in Basic Sciences","ror":"https://ror.org/00bzsst90","country_code":"IR","type":"education","lineage":["https://openalex.org/I161028277"]},{"id":"https://openalex.org/I4210117195","display_name":"HUN-REN Institute for Computer Science and Control","ror":"https://ror.org/0249v7n71","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210117195","https://openalex.org/I4387152226"]},{"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","IR"],"is_corresponding":false,"raw_author_name":"Manouchehr Zaker","raw_affiliation_strings":["Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran","Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, P.O. Box 63 Budapest, Hungary, H-1518","Department of Mathematics,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran","institution_ids":["https://openalex.org/I161028277"]},{"raw_affiliation_string":"Computer and Automation Research Institute Hungarian Academy of Sciences Budapest, P.O. Box 63 Budapest, Hungary, H-1518","institution_ids":["https://openalex.org/I7597260","https://openalex.org/I4210117195"]},{"raw_affiliation_string":"Department of Mathematics,","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.04545684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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/T13991","display_name":"Nuclear Receptors and Signaling","score":0.953499972820282,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13991","display_name":"Nuclear Receptors and Signaling","score":0.953499972820282,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9408000111579895,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9121000170707703,"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":0.8322405219078064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7455196380615234},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6702367663383484},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.502150297164917},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4090718626976013}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8322405219078064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7455196380615234},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6702367663383484},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.502150297164917},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4090718626976013},{"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:10.37236/595","is_oa":true,"landing_page_url":"https://doi.org/10.37236/595","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p108/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:10.37236/595","is_oa":true,"landing_page_url":"https://doi.org/10.37236/595","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p108/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":[{"id":"https://openalex.org/G6029566471","display_name":null,"funder_award_id":"K68322","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"}],"funders":[{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1570869955.pdf","grobid_xml":"https://content.openalex.org/works/W1570869955.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1975172784","https://openalex.org/W2022783208","https://openalex.org/W2043525791","https://openalex.org/W2050675734","https://openalex.org/W2071534536","https://openalex.org/W2476848496"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"family":[1],"${\\mathcal{F}}$":[2],"of":[3,46,57,68,144,151,159,188],"graphs":[4,58,69],"is":[5,111,140,155,173,184],"said":[6],"to":[7,129],"be":[8,130],"$(\\delta,\\chi)$-bounded":[9],"if":[10],"there":[11],"exists":[12],"a":[13,112,119,131,179,185],"function":[14],"$f(x)$":[15],"satisfying":[16],"$f(x)\\rightarrow":[17],"\\infty$":[18],"as":[19,74],"$x\\rightarrow":[20],"\\infty$,":[21],"such":[22],"that":[23,70,99,163],"for":[24,50,78,100,124,164],"any":[25,51,79,101,141,165],"graph":[26],"$G$":[27],"from":[28],"the":[29,40,66,90,94],"family,":[30,134],"one":[31],"has":[32],"$f(\\delta(G))\\leq":[33],"\\chi(G)$,":[34],"where":[35,135,153],"$\\delta(G)$":[36],"and":[37,43,104,121],"$\\chi(G)$":[38],"denotes":[39],"minimum":[41],"degree":[42],"chromatic":[44],"number":[45],"$G$,":[47],"respectively.":[48],"Also":[49],"set":[52,143],"$\\{H_1,":[53,136],"H_2,":[54,61,126,137],"\\ldots,":[55,62,81,127,138],"H_k\\}$":[56,139],"by":[59,93,97],"$Forb(H_1,":[60,125],"H_k)$":[63,128],"we":[64,86,117,147,177],"mean":[65],"class":[67],"contain":[71],"no":[72],"$H_i$":[73],"an":[75,156],"induced":[76],"subgraph":[77],"$i=1,":[80],"k$.":[82],"In":[83],"this":[84],"paper":[85],"first":[87],"answer":[88],"affirmatively":[89],"question":[91],"raised":[92],"second":[95],"author":[96],"showing":[98],"tree":[102],"$T$":[103],"positive":[105,166],"integer":[106,167],"$\\ell$,":[107,168],"$Forb(T,":[108],"K_{\\ell,":[109],"\\ell})$":[110],"$(\\delta,":[113,132,149,174],"\\chi)$-bounded":[114,133],"family.":[115],"Then":[116],"obtain":[118],"necessary":[120],"sufficient":[122],"condition":[123],"given":[142],"graphs.":[145,160,190],"Next":[146],"study":[148],"\\chi)$-boundedness":[150],"$Forb({\\mathcal{C}})$":[152],"${\\mathcal{C}}$":[154,183],"infinite":[157],"collection":[158,186],"We":[161],"show":[162,178],"$Forb(K_{\\ell,\\ell},":[169],"C_6,":[170],"C_8,":[171],"\\ldots)$":[172],"\\chi)$-bounded.":[175],"Finally":[176],"similar":[180],"result":[181],"when":[182],"consisting":[187],"unicyclic":[189]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
