{"id":"https://openalex.org/W4402705147","doi":"https://doi.org/10.37236/14093","title":"Colorful Fractional Helly Theorem via Weak Saturation","display_name":"Colorful Fractional Helly Theorem via Weak Saturation","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W4402705147","doi":"https://doi.org/10.37236/14093"},"language":"en","primary_location":{"id":"doi:10.37236/14093","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14093","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p29/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p29/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086849646","display_name":"Debsoumya Chakraborti","orcid":null},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Debsoumya Chakraborti","raw_affiliation_strings":["University College London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University College London","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102834292","display_name":"Minho Cho","orcid":"https://orcid.org/0000-0002-7751-2165"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Minho Cho","raw_affiliation_strings":["KIAS"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KIAS","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080229875","display_name":"Jinha Kim","orcid":"https://orcid.org/0000-0001-5982-7836"},"institutions":[{"id":"https://openalex.org/I4210092150","display_name":"Chonnam National University Hospital","ror":"https://ror.org/00f200z37","country_code":"KR","type":"healthcare","lineage":["https://openalex.org/I111277659","https://openalex.org/I4210092150"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jinha Kim","raw_affiliation_strings":["Chonnam National University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chonnam National University","institution_ids":["https://openalex.org/I4210092150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100615032","display_name":"Minki Kim","orcid":"https://orcid.org/0000-0002-9390-7255"},"institutions":[{"id":"https://openalex.org/I4210122665","display_name":"Gist (Czechia)","ror":"https://ror.org/0233hap27","country_code":"CZ","type":"company","lineage":["https://openalex.org/I4210122665"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Minki Kim","raw_affiliation_strings":["GIST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GIST","institution_ids":["https://openalex.org/I4210122665"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0161826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9929999709129333,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.5746558904647827},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.5465982556343079},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4982306957244873},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3391745388507843}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5746558904647827},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.5465982556343079},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4982306957244873},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3391745388507843}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/14093","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14093","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p29/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2408.15093","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2408.15093","pdf_url":"https://arxiv.org/pdf/2408.15093","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,"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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2408.15093","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2408.15093","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,"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":"doi:10.37236/14093","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14093","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p29/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1628183958","display_name":null,"funder_award_id":"947978","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G3108592684","display_name":null,"funder_award_id":"IBS-R029-C1","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5758617376","display_name":null,"funder_award_id":"IBS-R029-C1","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G6777733192","display_name":null,"funder_award_id":"IBS-R029-C4","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G7257815771","display_name":null,"funder_award_id":"NRF-2022R1F1A1063424","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8735294814","display_name":null,"funder_award_id":"IBS-R029-C4","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320326441","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402705147.pdf","grobid_xml":"https://content.openalex.org/works/W4402705147.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Two":[0],"celebrated":[1],"extensions":[2],"of":[3,31,43,90,112],"the":[4,9,14,24,28,32,35,44,54,77,87,101,113,118],"classical":[5,64],"Helly's":[6],"theorem":[7,12,57,80,121],"are":[8,84],"fractional":[10,33,55,78,119],"Helly":[11,16,37,56,79,120],"and":[13,20,34,58,81,122],"colorful":[15,36,60,124],"theorem.":[17],"Bulavka,":[18],"Goodarzi,":[19],"Tancer":[21],"recently":[22],"established":[23],"optimal":[25,114],"bound":[26],"for":[27,100,116],"unified":[29],"generalization":[30],"theorems":[38],"using":[39,127],"a":[40,63],"colored":[41],"extension":[42],"exterior":[45,128],"algebra.":[46,129],"In":[47],"this":[48],"paper,":[49],"we":[50],"combinatorially":[51],"reduce":[52],"both":[53,117],"its":[59,123],"version":[61,125],"to":[62],"problem":[65],"in":[66,86],"extremal":[67],"combinatorics":[68],"known":[69,85],"as":[70],"weak":[71,82,103],"saturation.":[72],"No":[73],"such":[74],"results":[75],"connecting":[76],"saturation":[83,104],"long":[88],"history":[89],"literature.":[91],"These":[92],"reductions,":[93],"along":[94],"with":[95],"basic":[96],"linear":[97],"algebraic":[98],"arguments":[99],"reduced":[102],"problems,":[105],"let":[106],"us":[107],"give":[108],"new":[109],"short":[110],"proofs":[111],"bounds":[115],"without":[126]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}