{"id":"https://openalex.org/W7161176232","doi":"https://doi.org/10.48550/arxiv.2605.12634","title":"Cover-free families on graphs","display_name":"Cover-free families on graphs","publication_year":2026,"publication_date":"2026-05-12","ids":{"openalex":"https://openalex.org/W7161176232","doi":"https://doi.org/10.48550/arxiv.2605.12634"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.12634","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.12634","pdf_url":"https://arxiv.org/pdf/2605.12634","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/2605.12634","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136117140","display_name":"Prangya Parida","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Parida, Prangya","raw_affiliation_strings":["Department of Mathematics and Statistics , University of Ottawa , Ottawa , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , University of Ottawa , Ottawa , Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010007126","display_name":"Lucia Moura","orcid":"https://orcid.org/0000-0003-1763-2584","observed_orcids":["https://orcid.org/0000-0003-1763-2584"]},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Moura, Lucia","raw_affiliation_strings":["Department of Mathematics and Statistics , University of Ottawa , Ottawa , Canada","School of Electrical Engineering and Computer Science , University of Ottawa , Ottawa , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , University of Ottawa , Ottawa , Canada","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science , University of Ottawa , Ottawa , Canada","institution_ids":["https://openalex.org/I153718931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I153718931"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.6039999723434448,"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":0.6039999723434448,"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":0.385699987411499,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.005799999926239252,"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/cover-free-families","display_name":"cover-free families","score":0.9810000061988831},{"id":"https://openalex.org/keywords/sperner-families","display_name":"Sperner families","score":0.7850000262260437},{"id":"https://openalex.org/keywords/hypergraphs","display_name":"hypergraphs","score":0.8579999804496765},{"id":"https://openalex.org/keywords/extremal-set-theory","display_name":"extremal set theory","score":0.8259999752044678},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"upper and lower bounds","score":0.6370000243186951},{"id":"https://openalex.org/keywords/star-graphs","display_name":"star graphs","score":0.7820000052452087},{"id":"https://openalex.org/keywords/cycle-graphs","display_name":"cycle graphs","score":0.5440000295639038},{"id":"https://openalex.org/keywords/wheel-graphs","display_name":"wheel graphs","score":0.9039999842643738},{"id":"https://openalex.org/keywords/paths","display_name":"paths","score":0.48899999260902405},{"id":"https://openalex.org/keywords/chromatic-number","display_name":"chromatic number","score":0.6549999713897705},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.48899999260902405},{"id":"https://openalex.org/keywords/extremal-hypergraph-theory","display_name":"extremal hypergraph theory","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8637999892234802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.796999990940094},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5281000137329102},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5092999935150146},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5069000124931335},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.4830000102519989},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.3977999985218048},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3864000141620636},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2612000107765198}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.12634","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.12634","pdf_url":"https://arxiv.org/pdf/2605.12634","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.2605.12634","doi":"https://doi.org/10.48550/arxiv.2605.12634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12634","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:2605.12634","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.12634","pdf_url":"https://arxiv.org/pdf/2605.12634","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7161176232.pdf","grobid_xml":"https://content.openalex.org/works/W7161176232.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4361866086"],"related_works":["https://openalex.org/W7208733076","https://openalex.org/W2172288732","https://openalex.org/W38327574","https://openalex.org/W2047840070","https://openalex.org/W2951077088","https://openalex.org/W2052666099","https://openalex.org/W6963932974","https://openalex.org/W2030083434","https://openalex.org/W2244455306","https://openalex.org/W7217763732"],"abstract_inverted_index":{"A":[0,104],"family":[1,18,109,138,253],"of":[2,4,24,110,112,119,124,139,141,152,155,161,254,281],"subsets":[3,99,111,125,140,156],"a":[5,8,40,43,49,55,92,108,113,122,133,137,142,153,184,188,294],"$t$-set":[6,44,114,143],"is":[7,19,51,107,136,147],"\\emph{$d$-cover-free":[9],"family}":[10],"or":[11],"$d$-CFF":[12,41],"if":[13],"no":[14,242],"subset":[15,168],"in":[16,21,100,128,169],"the":[17,22,33,52,101,150,170,177,246,258],"contained":[20,127],"union":[23,151],"any":[25,166,212,237],"$d$":[26],"other":[27,167],"subsets.":[28,47],"Let":[29,172],"$t(d,":[30],"n)$":[31,106,135,186,198,234],"denote":[32,176],"minimum":[34,178],"$t$":[35,179],"for":[36,180,211,223,236,250,262,279],"which":[37,181],"there":[38,182],"exists":[39],"on":[42,86,297],"with":[45,241,245,319],"$n$":[46,68,320],"Since":[48],"$1$-CFF":[50,88],"same":[53],"as":[54,67,132,284],"Sperner":[56],"family,":[57],"using":[58,91],"Sperner's":[59],"theorem,":[60],"we":[61,205],"get":[62],"$t(1,":[63,228],"n)":[64,229],"\\sim":[65],"\\log_{2}(n)$":[66],"grows.":[69],"Erd\u00f6s,":[70],"Frankl,":[71],"and":[72,89,149,174,187,199,216,220,257,273,289,313,317],"F\u00fcredi":[73],"(JCTA,":[74],"1982)":[75],"proved":[76],"that":[77,116,145],"$3.106\\log_{2}(n)":[78],"<":[79,81],"t(2,n)":[80],"5.512\\log_{2}(n)$.":[82],"This":[83],"paper":[84],"focuses":[85],"generalizing":[87],"$2$-CFF":[90],"graph":[93,214,239],"$G$":[94,120,162,215,240],"where":[95,131,311],"vertices":[96],"correspond":[97],"to":[98,158],"set":[102],"system.":[103],"$G$-Sperner$(t,":[105,185],"such":[115,144,283],"each":[117,129,159],"edge":[118,160],"specifies":[121],"pair":[123,154],"not":[126,164],"other,":[130],"$G$-CFF$(t,":[134,189],"it":[146],"$G$-Sperner":[148],"corresponding":[157],"does":[163],"contain":[165],"family.":[171],"$t_s(G)$":[173],"$t(G)$":[175],"exist":[183],"n)$,":[190],"respectively.":[191],"In":[192,292],"this":[193],"way,":[194],"$t_s(K_n)":[195],"=":[196,201,208],"t(1,":[197,209],"$t(K_n)":[200],"t(2,":[202,233],"n)$.":[203],"Firstly,":[204],"prove":[206],"$t_s(G)":[207],"\u03c7(G))$":[210],"simple":[213,238],"provide":[217],"various":[218],"upper":[219,259,277],"lower":[221,247],"bounds":[222,269,278],"$t(G)$.":[224],"The":[225],"\\emph{trivial":[226],"bound},":[227],"\\leq":[230,232,303,305,307],"t(G)":[231],"holds":[235],"isolated":[243],"vertex,":[244],"bound":[248,260],"tight":[249,261],"an":[251],"infinite":[252],"star":[255],"graphs":[256,282],"complete":[263],"graphs.":[264,291],"We":[265],"study":[266],"when":[267],"these":[268],"can":[270],"be":[271],"improved":[272],"give":[274],"better":[275],"constructive":[276],"families":[280],"stars,":[285],"paths,":[286],"cycles,":[287],"wheels,":[288],"windmill":[290],"particular,":[293],"construction":[295],"based":[296],"mixed-radix":[298],"Gray":[299],"codes":[300],"yields":[301],"$\\log_{2}(n)":[302],"t(P_n)":[304],"t(C_n)":[306],"1.893\\log_{2}(n)":[308],"+":[309],"\\mathcal{O}(1)$":[310],"$P_n$":[312],"$C_n$":[314],"are":[315],"paths":[316],"cycles":[318],"vertices.":[321]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-05-15T00:00:00"}