{"id":"https://openalex.org/W4417134749","doi":"https://doi.org/10.1137/25m1767200","title":"Refuting Perfect Matchings in Spectral Expanders Is Hard","display_name":"Refuting Perfect Matchings in Spectral Expanders Is Hard","publication_year":2026,"publication_date":"2026-06-12","ids":{"openalex":"https://openalex.org/W4417134749","doi":"https://doi.org/10.1137/25m1767200"},"language":"en","primary_location":{"id":"doi:10.1137/25m1767200","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1767200","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.07700","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053221778","display_name":"Ari Biswas","orcid":"https://orcid.org/0000-0001-6412-844X"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ari Biswas","raw_affiliation_strings":["University of Warwick, Coventry, CV4 7AL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick, Coventry, CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074609284","display_name":"Rajko Nenadov","orcid":"https://orcid.org/0009-0003-3777-021X"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Rajko Nenadov","raw_affiliation_strings":["School of Computer Science, University of Canterbury, Christchurch, 8140 New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Canterbury, Christchurch, 8140 New Zealand","institution_ids":["https://openalex.org/I185492890"]}]}],"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":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04606091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"2","first_page":"905","last_page":"918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.3885999917984009,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.3885999917984009,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.149399995803833,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.11969999969005585,"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/mathematical-proof","display_name":"Mathematical proof","score":0.6590999960899353},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5805000066757202},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.5590999722480774},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4699999988079071},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.35030001401901245},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3474000096321106}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7203999757766724},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6590999960899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6021000146865845},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5805000066757202},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.5590999722480774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5113000273704529},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.35030001401901245},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.3377000093460083},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2522999942302704}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/25m1767200","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1767200","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:arXiv.org:2506.07700","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.07700","pdf_url":"https://arxiv.org/pdf/2506.07700","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2506.07700","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},{"id":"doi:10.48550/arxiv.2506.07700","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.07700","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.07700","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.07700","pdf_url":"https://arxiv.org/pdf/2506.07700","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"work":[1],"studies":[2],"the":[3,7,23,50,69],"complexity":[4],"of":[5,9,20,29],"refuting":[6,41],"existence":[8],"a":[10,79],"perfect":[11,42],"matching":[12],"in":[13,22,44,49],"spectral":[14,81],"expanders":[15],"with":[16,54,59,78],"an":[17],"odd":[18],"number":[19],"vertices,":[21],"Polynomial":[24],"Calculus":[25],"(PC)":[26],"and":[27,35],"Sum":[28],"Squares":[30],"(SoS)":[31],"proof":[32,52],"system.":[33],"Austrin":[34],"Risse":[36],"[SODA,":[37],"2021]":[38],"showed":[39],"that":[40],"matchings":[43],"sparse":[45],"$d$-regular":[46,76],"\\emph{random}":[47],"graphs,":[48],"above":[51],"systems,":[53],"high":[55],"probability":[56],"requires":[57],"proofs":[58],"degree":[60],"$\u03a9(n/\\log":[61],"n)$.":[62],"We":[63],"extend":[64],"their":[65],"result":[66],"by":[67],"showing":[68],"same":[70],"lower":[71],"bound":[72],"holds":[73],"for":[74],"\\emph{all}":[75],"graphs":[77],"mild":[80],"gap.":[82]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}