{"id":"https://openalex.org/W7225466366","doi":"https://doi.org/10.5281/zenodo.24045056","title":"Negative correlation of edges in the uniform random forest of complete bipartite and complete multipartite graphs","display_name":"Negative correlation of edges in the uniform random forest of complete bipartite and complete multipartite graphs","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225466366","doi":"https://doi.org/10.5281/zenodo.24045056"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24045056","doi":"https://doi.org/10.5281/zenodo.24045056","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24045056","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24045056","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017497939","display_name":"William Huanshan Chuang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chuang, William Huanshan","raw_affiliation_strings":["Logarcheon Inc"],"raw_orcid":"https://orcid.org/0009-0008-0796-9478","affiliations":[{"raw_affiliation_string":"Logarcheon Inc","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017497939"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8682000041007996,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8682000041007996,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.05249999836087227,"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/T11476","display_name":"Graph theory and applications","score":0.03779999911785126,"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/complete-bipartite-graphs","display_name":"complete bipartite graphs","score":0.9190000295639038},{"id":"https://openalex.org/keywords/complete-multipartite-graphs","display_name":"complete multipartite graphs","score":1.0},{"id":"https://openalex.org/keywords/lagrange-inversion","display_name":"Lagrange inversion","score":0.8849999904632568},{"id":"https://openalex.org/keywords/laguerre-polynomials","display_name":"Laguerre polynomials","score":0.9739999771118164},{"id":"https://openalex.org/keywords/matching-polynomial","display_name":"matching polynomial","score":0.718999981880188},{"id":"https://openalex.org/keywords/rayleigh-criterion","display_name":"Rayleigh criterion","score":0.8050000071525574},{"id":"https://openalex.org/keywords/lean-4-formal-verification","display_name":"Lean 4 formal verification","score":0.8740000128746033}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.861299991607666},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8317000269889832},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5428000092506409},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.5281000137329102},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5212000012397766},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4629000127315521},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4611999988555908},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.3269999921321869},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3140999972820282},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.31119999289512634},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.2980000078678131},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.28130000829696655},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.27230000495910645},{"id":"https://openalex.org/C103257674","wikidata":"https://www.wikidata.org/wiki/Q6934937","display_name":"Multiple edges","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24045056","doi":"https://doi.org/10.5281/zenodo.24045056","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24045056","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:10.5281/zenodo.24045057","doi":"https://doi.org/10.5281/zenodo.24045057","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24045057","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:10.5281/zenodo.24045056","doi":"https://doi.org/10.5281/zenodo.24045056","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24045056","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7224118643","https://openalex.org/W7201845893","https://openalex.org/W7210294250","https://openalex.org/W2032875198","https://openalex.org/W2166935116","https://openalex.org/W2949117595","https://openalex.org/W7135137429","https://openalex.org/W7172343414","https://openalex.org/W7215878311","https://openalex.org/W2050013290"],"abstract_inverted_index":{"A":[0],"conjecture":[1,216],"of":[2,5,16,48,78,85,122,151,175,192,232],"Kahn":[3],"and":[4,75,109,124,204,208,238,250],"Winkler,":[6],"open":[7],"since":[8],"2000,":[9],"asserts":[10],"that":[11,130,217],"any":[12,120,125],"two":[13,32,128],"distinct":[14,49],"edges":[15,50,129,234],"a":[17,86,132,169,181,261],"finite":[18],"graph":[19,39],"are":[20,134],"negatively":[21,53,135],"correlated":[22],"under":[23,180],"the":[24,68,83,140,149,154,173,176,190,201,205,213,218],"uniform":[25],"measure":[26],"on":[27,99,189,241,260],"its":[28],"forests.":[29],"We":[30,215],"prove":[31],"cases.":[33,112],"First,":[34],"for":[35,55,114,224],"every":[36,46,60,115,225],"complete":[37,116,163],"bipartite":[38],"K_{a,b}":[40],"with":[41,105,119,153,245,269],"a,":[42],"b":[43],"\u2265":[44],"2,":[45],"pair":[47,61,80],"is":[51,94,103,172,196,221,264],"strictly":[52],"correlated;":[54],"min(a,":[56],"b)":[57],"=":[58],"1":[59],"gives":[62,212],"equality.":[63],"Two-variable":[64],"Lagrange":[65],"inversion":[66],"expresses":[67],"forest":[69],"counts":[70,148],"through":[71],"rescaled":[72],"Laguerre":[73],"polynomials,":[74],"each":[76,101],"type":[77],"edge":[79],"reduces":[81],"to":[82,96,247],"sign":[84],"concave":[87],"quadratic":[88,102],"in":[89,235,266],"one":[90,160,253],"ratio.":[91],"This":[92],"ratio":[93],"confined":[95],"an":[97],"interval":[98],"which":[100,227],"positive,":[104],"no":[106,110,187],"asymptotic":[107],"regime":[108],"exceptional":[111],"Second,":[113],"multipartite":[117,164],"graph,":[118,226],"number":[121],"parts":[123],"part":[126],"sizes,":[127],"share":[131],"vertex":[133,141,155,219],"correlated.":[136],"The":[137],"proof":[138],"introduces":[139],"polynomial":[142,179,220],"\u03a3_S":[143],"F(G/S)":[144,147],"t^S,":[145],"where":[146],"forests":[150],"G":[152],"set":[156],"S":[157],"merged":[158],"into":[159],"vertex.":[161],"For":[162],"graphs":[165,244],"this":[166],"polynomial,":[167],"after":[168],"fixed":[170],"shift,":[171],"image":[174],"vertex-weighted":[177],"matching":[178],"linear":[182],"operator":[183],"whose":[184],"symbol":[185],"has":[186],"zeros":[188],"product":[191],"upper":[193],"half-planes.":[194],"It":[195],"therefore":[197],"real":[198,222],"stable":[199,223],"by":[200],"Heilmann\u2013Lieb":[202],"theorem":[203,263],"Borcea\u2013Br\u00e4nd\u00e9n":[206],"characterisation,":[207],"Br\u00e4nd\u00e9n\u2019s":[209],"Rayleigh":[210],"criterion":[211],"inequality.":[214],"would":[228],"give":[229],"negative":[230],"correlation":[231],"adjacent":[233],"all":[236,242],"graphs,":[237],"report":[239],"checks":[240],"1,244":[243],"3":[246],"7":[248],"vertices":[249],"at":[251],"least":[252],"edge.":[254],"Every":[255],"algebraic":[256],"step":[257],"not":[258],"resting":[259],"cited":[262],"verified":[265],"Lean":[267],"4":[268],"Mathlib.":[270]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}