{"id":"https://openalex.org/W7204671255","doi":"https://doi.org/10.48550/arxiv.2608.27179","title":"On Eigenvalue Bounds for Bounded Genus Graphs and Minor-Free Graphs","display_name":"On Eigenvalue Bounds for Bounded Genus Graphs and Minor-Free Graphs","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204671255","doi":"https://doi.org/10.48550/arxiv.2608.27179"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27179","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27179","pdf_url":"https://arxiv.org/pdf/2608.27179","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.27179","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001011989","display_name":"Benedikt Kolbe","orcid":"https://orcid.org/0009-0005-0440-4912","observed_orcids":["https://orcid.org/0009-0005-0440-4912"]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4391767997","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36","country_code":"DE","type":"facility","lineage":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kolbe, Benedikt","raw_affiliation_strings":["Hausdorff Center for Mathematics , University of Bonn. This"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics , University of Bonn. This","institution_ids":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081824405","display_name":"Jack Spalding-Jamieson","orcid":"https://orcid.org/0000-0002-1209-4345","observed_orcids":["https://orcid.org/0000-0002-1209-4345"]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4391767997","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36","country_code":"DE","type":"facility","lineage":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Spalding-Jamieson, Jack","raw_affiliation_strings":["Hausdorff Center for Mathematics , University of Bonn. This"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics , University of Bonn. This","institution_ids":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11476","display_name":"Graph theory and applications","score":0.4636000096797943,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.4636000096797943,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.17960000038146973,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.09780000150203705,"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/laplacian-eigenvalues","display_name":"Laplacian eigenvalues","score":0.7599999904632568},{"id":"https://openalex.org/keywords/second-smallest-eigenvalue","display_name":"second smallest eigenvalue","score":0.6729999780654907},{"id":"https://openalex.org/keywords/spectral-partitioning","display_name":"spectral partitioning","score":0.6700000166893005},{"id":"https://openalex.org/keywords/orientable-surfaces","display_name":"orientable surfaces","score":0.8790000081062317},{"id":"https://openalex.org/keywords/normalized-laplacian-eigenvalues","display_name":"normalized Laplacian eigenvalues","score":0.9610000252723694},{"id":"https://openalex.org/keywords/steklov-eigenvalues","display_name":"Steklov eigenvalues","score":1.0},{"id":"https://openalex.org/keywords/lovasz-local-lemma","display_name":"Lov\u00e1sz local lemma","score":0.9620000123977661},{"id":"https://openalex.org/keywords/graph-partitioning","display_name":"graph partitioning","score":0.4230000078678131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7577000260353088},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7170000076293945},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7052000164985657},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5874000191688538},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5824000239372253},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5360000133514404},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.5131999850273132},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5037999749183655},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.46059998869895935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4499000012874603},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43720000982284546},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.4318999946117401},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.40799999237060547},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.36649999022483826},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3517000079154968},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.3192000091075897},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.25429999828338623},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27179","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27179","pdf_url":"https://arxiv.org/pdf/2608.27179","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.27179","doi":"https://doi.org/10.48550/arxiv.2608.27179","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27179","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.27179","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27179","pdf_url":"https://arxiv.org/pdf/2608.27179","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204671255.pdf","grobid_xml":"https://content.openalex.org/works/W7204671255.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4384692454","https://openalex.org/W4414895654","https://openalex.org/W7126190533"],"related_works":["https://openalex.org/W2153940758","https://openalex.org/W2949285221","https://openalex.org/W3022762247","https://openalex.org/W2963487913","https://openalex.org/W2963857009","https://openalex.org/W3015735847","https://openalex.org/W7096741620","https://openalex.org/W1977994523","https://openalex.org/W4200507174","https://openalex.org/W7100136222"],"abstract_inverted_index":{"In":[0,31,72],"this":[1],"paper,":[2],"we":[3,45,91],"resolve":[4],"a":[5,35,89],"30-year-old":[6],"conjecture":[7],"of":[8,15,27,51,69,117,120,142,170,176],"Spielman":[9],"and":[10,41,105,172],"Teng":[11],"concerning":[12],"the":[13,16,48,154,158,177],"performance":[14],"spectral":[17],"partitioning":[18],"method":[19],"on":[20,23,96,101],"graphs":[21,68,112,127,138,166],"embeddable":[22],"an":[24,62,168],"orientable":[25],"surface":[26],"genus":[28],"$g\\ge":[29],"1$.":[30],"particular,":[32],"for":[33,66,81,110,115,125,136,145,150,153,164],"such":[34],"graph":[36],"$G$":[37],"with":[38],"$n$":[39],"vertices":[40],"maximum":[42],"degree":[43],"$\u0394$,":[44],"show":[46],"that":[47],"second-smallest":[49],"eigenvalue":[50,64],"its":[52],"Laplacian":[53,97,103],"matrix":[54],"satisfies":[55],"$\u03bb_2(L_G)\\lesssim\u0394\\frac":[56],"g":[57],"n$.":[58],"We":[59],"also":[60,100],"obtain":[61,92],"improved":[63],"bound":[65],"$K_h$-minor-free":[67,126,165],"$\u03bb_2(L_G)\\lesssim\u0394\\frac{h^2(\\log":[70],"h)^2}n$.":[71],"fact,":[73],"our":[74,123,162],"results":[75,80,109,124],"directly":[76],"prove":[77],"much":[78],"stronger":[79],"reweighted":[82,86,151],"eigenvalues,":[83,98,121],"including":[84],"higher":[85],"eigenvalues.":[87,107],"As":[88],"consequence,":[90],"bounds":[93,141,149],"not":[94],"just":[95],"but":[99],"normalized":[102,143],"eigenvalues":[104,144,152],"Steklov":[106],"Our":[108,134],"genus-$g$":[111,137],"are":[113,128],"optimal":[114,129],"all":[116],"these":[118],"kinds":[119],"while":[122,161],"up":[130],"to":[131,148],"$\\log(h)$":[132],"factors.":[133],"techniques":[135,163],"bootstrap":[139],"bounded-degree":[140,159],"entire":[146],"classes":[147,156],"same":[155],"without":[157],"limitation,":[160],"generalize":[167],"argument":[169],"Korhonen":[171],"Lokshtanov,":[173],"making":[174],"use":[175],"Lov\u00e1sz":[178],"local":[179],"lemma.":[180]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-30T00:00:00"}