{"id":"https://openalex.org/W7225036076","doi":"https://doi.org/10.6084/m9.figshare.34876788","title":"On separators in K_h-minor-free graphs","display_name":"On separators in K_h-minor-free graphs","publication_year":2026,"publication_date":"2026-11-01","ids":{"openalex":"https://openalex.org/W7225036076","doi":"https://doi.org/10.6084/m9.figshare.34876788"},"language":"en","primary_location":{"id":"doi:10.6084/m9.figshare.34876788","doi":"https://doi.org/10.6084/m9.figshare.34876788","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34876788","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.6084/m9.figshare.34876788","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160285480","display_name":"Lin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160285480"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0012000000569969416,"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":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/graph-separators","display_name":"graph separators","score":0.7699999809265137},{"id":"https://openalex.org/keywords/graph-minors","display_name":"graph minors","score":0.7070000171661377},{"id":"https://openalex.org/keywords/treewidth","display_name":"treewidth","score":0.5809999704360962},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.3580000102519989}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46160000562667847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4471000134944916},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4115000069141388},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4002000093460083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39469999074935913},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3474999964237213},{"id":"https://openalex.org/C191916993","wikidata":"https://www.wikidata.org/wiki/Q362019","display_name":"Numbering","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3276999890804291},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32589998841285706},{"id":"https://openalex.org/C2776902872","wikidata":"https://www.wikidata.org/wiki/Q352410","display_name":"ASTRA","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.298799991607666},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C41458344","wikidata":"https://www.wikidata.org/wiki/Q732577","display_name":"Publication","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C185004128","wikidata":"https://www.wikidata.org/wiki/Q3011536","display_name":"Separator (oil production)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.6084/m9.figshare.34876788","doi":"https://doi.org/10.6084/m9.figshare.34876788","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34876788","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.6084/m9.figshare.34876788.v1","doi":"https://doi.org/10.6084/m9.figshare.34876788.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34876788.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.6084/m9.figshare.34876788","doi":"https://doi.org/10.6084/m9.figshare.34876788","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34876788","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7224896201","https://openalex.org/W7160599944","https://openalex.org/W7224206641","https://openalex.org/W2089807138","https://openalex.org/W3153582419","https://openalex.org/W1550106322","https://openalex.org/W7154340587","https://openalex.org/W4414895654","https://openalex.org/W4416966110","https://openalex.org/W2145062394"],"abstract_inverted_index":{"This":[0,105],"manuscript":[1,40,106],"records":[2],"possible":[3],"improvements":[4],"of":[5,23,47,93,114],"the":[6,21,26,34,69,82,94,112,115],"constants":[7],"in":[8,15,68,126],"Xinheng":[9],"Lin\u2019s":[10],"arXiv":[11],"preprint,":[12,25],"\u201cOn":[13],"separators":[14],"K_t-minor-free":[16],"graphs\u201d":[17],"(arXiv:2610.40270,":[18],"https://arxiv.org/abs/2610.40270).Building":[19],"on":[20],"results":[22],"that":[24],"author":[27,86,119],"used":[28],"ChatGPT":[29],"6":[30],"Astra":[31,103],"to":[32,79,110,123],"develop":[33],"proposed":[35,71],"improvements.":[36,117],"In":[37],"particular,":[38],"this":[39,91],"proposes":[41],"a":[42,127],"balanced":[43],"vertex":[44],"separator":[45],"bound":[46],"min{ceil(n/3),":[48],"2.7278(h\u22121)\u221an}":[49],"for":[50],"every":[51,57],"integer":[52],"h":[53],"\u2265":[54],"3":[55],"and":[56,64,76],"n-vertex":[58],"K_h-minor-free":[59],"graph,":[60],"with":[61],"further":[62],"refinements":[63],"lower":[65],"bounds":[66],"discussed":[67],"text.The":[70],"proof":[72],"is":[73,107],"substantially":[74],"longer":[75],"more":[77],"difficult":[78],"read":[80],"than":[81],"original":[83],"proof.":[84],"The":[85,118],"has":[87],"not":[88,121],"personally":[89],"checked":[90],"version":[92],"manuscript;":[95],"its":[96],"review":[97],"was":[98],"carried":[99],"out":[100],"using":[101],"GPT-6":[102],"(Ultra).":[104],"intended":[108],"only":[109],"record":[111],"possibility":[113],"stated":[116],"does":[120],"intend":[122],"publish":[124],"it":[125],"formal":[128],"journal.":[129]},"counts_by_year":[],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2026-11-02T00:00:00"}