{"id":"https://openalex.org/W2005449342","doi":"https://doi.org/10.1137/070699482","title":"Hereditary Domination in Graphs: Characterization with Forbidden Induced Subgraphs","display_name":"Hereditary Domination in Graphs: Characterization with Forbidden Induced Subgraphs","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2005449342","doi":"https://doi.org/10.1137/070699482","mag":"2005449342"},"language":"en","primary_location":{"id":"doi:10.1137/070699482","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070699482","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5026437192","display_name":"\u0179solt Tuza","orcid":"https://orcid.org/0000-0003-3235-9221"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zsolt Tuza","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026437192"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6987,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.92522167,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"22","issue":"3","first_page":"849","last_page":"853"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9926999807357788,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9878000020980835,"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":0.8800091743469238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.783461332321167},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.6708723902702332},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5130811929702759},{"id":"https://openalex.org/keywords/distance-hereditary-graph","display_name":"Distance-hereditary graph","score":0.4625389575958252},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4536643624305725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4111782908439636},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2036246359348297},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.06621313095092773}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8800091743469238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.783461332321167},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.6708723902702332},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5130811929702759},{"id":"https://openalex.org/C147792647","wikidata":"https://www.wikidata.org/wiki/Q5282847","display_name":"Distance-hereditary graph","level":5,"score":0.4625389575958252},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4536643624305725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4111782908439636},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2036246359348297},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.06621313095092773}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070699482","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070699482","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.sztaki.hu:5419","is_oa":false,"landing_page_url":"http://eprints.sztaki.hu/5419/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401907","display_name":"SZTAKI Publication Repository (Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I7597260","host_organization_name":"Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I7597260"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ISI Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1992186598","https://openalex.org/W2003292013","https://openalex.org/W2028775537","https://openalex.org/W2030973065","https://openalex.org/W2092318469","https://openalex.org/W2149120814"],"related_works":["https://openalex.org/W4313325064","https://openalex.org/W1930073757","https://openalex.org/W4224270192","https://openalex.org/W1985038305","https://openalex.org/W1648368097","https://openalex.org/W2014608127","https://openalex.org/W91714901","https://openalex.org/W2124404826","https://openalex.org/W2032950096","https://openalex.org/W4286911546"],"abstract_inverted_index":{"The":[0],"leaf":[1,48,91,129],"graph":[2,6,27],"of":[3,14,34,55,66,70,93,108,125,131,143,161,192],"a":[4,11,25,43,179,205],"connected":[5,26,44,67,110,133,145],"is":[7,29,40,51,103,158],"obtained":[8],"by":[9,32,42,76,121,201,203],"joining":[10],"new":[12],"vertex":[13],"degree":[15],"one":[16],"to":[17,81],"each":[18],"noncutting":[19],"vertex.":[20],"We":[21],"prove":[22],"that":[23,135,181],"if":[24,100],"G":[28,39],"not":[30,74,137,165,173],"dominated":[31,41,75],"any":[33,77],"its":[35],"induced":[36,45,53,78,111,127,146],"paths,":[37],"then":[38,113],"subgraph":[46,54,79],"whose":[47],"graph,":[49],"too,":[50],"an":[52],"G.":[56],"It":[57],"follows":[58],"that,":[59],"for":[60,189],"every":[61],"nonempty":[62],"class":[63],"${\\cal":[64,101,116,139,150,167,170,195],"D}$":[65,84,102,168,171,196],"graphs,":[68],"all":[69,142,175],"the":[71,106,114,122,132,153,159,162,185,190],"minimal":[72],"graphs":[73,92,95,118,130,134],"isomorphic":[80],"some":[82,94],"$D\\in{\\cal":[83],"are":[85,119,136,148],"cycles":[86],"(of":[87],"well-determined":[88],"lengths)":[89],"and":[90,152],"$H\\notin{\\cal":[96],"D}$.":[97],"In":[98],"particular,":[99],"closed":[104],"under":[105],"operation":[107],"taking":[109],"subgraphs,":[112],"hereditarily":[115],"D}$-dominated":[117],"characterized":[120],"following":[123],"family":[124],"forbidden":[126],"subgraphs:":[128],"in":[138,149,166],"D}$,":[140,151],"but":[141],"their":[144],"subgraphs":[147],"cycle":[154],"$C_{t+2}$,":[155],"where":[156],"t":[157],"length":[160],"shortest":[163],"path":[164],"(if":[169],"does":[172],"contain":[174],"paths).":[176],"This":[177],"solves":[178],"problem":[180],"was":[182],"open":[183],"since":[184],"1980s.":[186],"A":[187],"solution":[188],"case":[191],"induced-hereditary":[193],"classes":[194],"has":[197],"been":[198],"found":[199],"simultaneously":[200],"Bacs\u00f3":[202],"applying":[204],"different":[206],"method.":[207]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
