{"id":"https://openalex.org/W7151019457","doi":"https://doi.org/10.48550/arxiv.2604.02796","title":"A polynomial bound for the minimal excluded minors for a surface","display_name":"A polynomial bound for the minimal excluded minors for a surface","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7151019457","doi":"https://doi.org/10.48550/arxiv.2604.02796"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.02796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02796","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.02796","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133029920","display_name":"Sarah Houdaigoui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Houdaigoui, Sarah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133047700","display_name":"Ken-ichi Kawarabayashi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kawarabayashi, Ken-ichi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"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":0.5907999873161316,"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":0.5907999873161316,"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":0.08760000020265579,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.0812000036239624,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7598999738693237},{"id":"https://openalex.org/keywords/contractible-space","display_name":"Contractible space","score":0.732699990272522},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6521999835968018},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5813999772071838},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.3531000018119812},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3456000089645386},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.3386000096797943},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.3357999920845032}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8756999969482422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8022000193595886},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7598999738693237},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.732699990272522},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6521999835968018},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5813999772071838},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4821000099182129},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.3386000096797943},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.26429998874664307}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.02796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02796","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.02796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02796","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"As":[0],"part":[1],"of":[2,16,33,61,125,133,172,186,210,231,257],"the":[3,14,54,59,83,89,98,123,126,146,149,156,162,241,273],"graph":[4],"minor":[5,182],"project,":[6],"Robertson":[7],"and":[8,69,88,152,191,205,252],"Seymour":[9,52],"showed":[10,193],"in":[11,22,207,238,254,277],"1990":[12],"that":[13,18,106,122,194,202,249],"class":[15],"graphs":[17],"can":[19,26],"be":[20,27,178],"embedded":[21],"a":[23,30,76,107,131,168,179,184,218,229,264,268],"given":[24],"surface":[25,132,185],"characterized":[28],"by":[29,74,120,216],"finite":[31],"set":[32],"minimal":[34,63,127,173,180],"excluded":[35,48,64,128,174,181],"minors.":[36,49,65,175],"However,":[37],"their":[38],"proof,":[39],"because":[40],"existential,":[41],"provides":[42],"no":[43],"explicit":[44],"information":[45],"about":[46],"these":[47],"In":[50,102,113],"1993,":[51],"established":[53],"first":[55],"upper":[56,78,109,153],"bound":[57,87,93,110,266],"on":[58],"order":[60,124],"such":[62],"Very":[66],"recently,":[67],"Houdaigoui":[68,190],"Kawarabayashi":[70,192],"improved":[71],"this":[72,81,86,114,118,214],"result":[73,143,215],"deriving":[75,278],"quasi-polynomial":[77],"bound.":[79,281],"Despite":[80],"progress,":[82],"gap":[84,147],"between":[85,148],"known":[90,150],"linear":[91],"lower":[92,151],"$\u03a9(g)$":[94],"(where":[95],"$g$":[96,135],"denotes":[97],"genus)":[99],"remains":[100],"substantial.":[101],"particular,":[103],"they":[104],"conjectured":[105,163],"polynomial":[108,280],"should":[111],"hold.":[112],"paper,":[115],"we":[116],"confirm":[117],"conjecture":[119],"showing":[121],"minors":[129],"for":[130,138,183,221],"genus":[134,188],"is":[136,272],"$O(g^{8+\\varepsilon})$":[137],"every":[139],"$\\varepsilon":[140],">0$.":[141],"This":[142,259],"significantly":[144],"narrows":[145],"bounds,":[154],"bringing":[155],"asymptotic":[157],"behavior":[158],"much":[159],"closer":[160],"to":[161,262],"optimum.":[164],"Our":[165],"approach":[166],"introduces":[167],"new":[169,275],"forbidden":[170],"structure":[171],"Let":[176],"$G$":[177,195],"Euler":[187],"$g$.":[189],"contains":[196,244],"$O(\\log":[197,245],"g)$":[198],"pairwise":[199],"disjoint":[200,247],"cycles":[201,248],"are":[203,250],"contractible":[204,223,251],"nested":[206,253],"some":[208,255],"embedding":[209,256],"$G$.":[211,258],"We":[212],"strengthen":[213],"proving":[217],"separator-based":[219],"variant:":[220],"any":[222],"subgraph":[224,242],"$H":[225],"\\subseteq":[226],"G$":[227],"with":[228,267],"separator":[230],"size":[232],"$s$":[233],"(with":[234],"$H$":[235,243],"completely":[236],"contained":[237],"one":[239],"side),":[240],"s)$":[246],"allows":[260],"us":[261],"replace":[263],"genus-dependent":[265],"separator-dependent":[269],"one,":[270],"which":[271],"main":[274],"ingredient":[276],"our":[279]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-07T00:00:00"}