{"id":"https://openalex.org/W2160146419","doi":"https://doi.org/10.37236/4137","title":"A Note on Covering Edge Colored Hypergraphs by Monochromatic Components","display_name":"A Note on Covering Edge Colored Hypergraphs by Monochromatic Components","publication_year":2014,"publication_date":"2014-05-13","ids":{"openalex":"https://openalex.org/W2160146419","doi":"https://doi.org/10.37236/4137","mag":"2160146419"},"language":"en","primary_location":{"id":"doi:10.37236/4137","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4137","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p33/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p33/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101970850","display_name":"Shinya Fujita","orcid":"https://orcid.org/0000-0001-8812-8321"},"institutions":[{"id":"https://openalex.org/I89630735","display_name":"Yokohama City University","ror":"https://ror.org/0135d1r83","country_code":"JP","type":"education","lineage":["https://openalex.org/I89630735"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shinya Fujita","raw_affiliation_strings":["Yokohama City University"],"affiliations":[{"raw_affiliation_string":"Yokohama City University","institution_ids":["https://openalex.org/I89630735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045129685","display_name":"Michitaka Furuya","orcid":"https://orcid.org/0000-0003-0991-6122"},"institutions":[{"id":"https://openalex.org/I89630735","display_name":"Yokohama City University","ror":"https://ror.org/0135d1r83","country_code":"JP","type":"education","lineage":["https://openalex.org/I89630735"]},{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU","JP"],"is_corresponding":false,"raw_author_name":"Michitaka Furuya","raw_affiliation_strings":["International College of Arts and Sciences Yokohama City University 22-2, Seto, Kanazawa-ku Yokohama, 236-0027, Japan","Alfr\u00e9d R\u00e9nyi Intitute of Mathematics Hungarian Academy of Sciences 1364 Budapest, P.O. Box 127, Hungary","Dept. of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka, Sinjuku-ku Tokyo 162-8601, Japan"],"affiliations":[{"raw_affiliation_string":"International College of Arts and Sciences Yokohama City University 22-2, Seto, Kanazawa-ku Yokohama, 236-0027, Japan","institution_ids":["https://openalex.org/I89630735"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Intitute of Mathematics Hungarian Academy of Sciences 1364 Budapest, P.O. Box 127, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Dept. of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka, Sinjuku-ku Tokyo 162-8601, Japan","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020847160","display_name":"Andr\u00e1s Gy\u00e1rf\u00e1s","orcid":"https://orcid.org/0000-0001-6173-1008"},"institutions":[{"id":"https://openalex.org/I89630735","display_name":"Yokohama City University","ror":"https://ror.org/0135d1r83","country_code":"JP","type":"education","lineage":["https://openalex.org/I89630735"]},{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU","JP"],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Gy\u00e1rf\u00e1s","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Intitute of Mathematics Hungarian Academy of Sciences 1364 Budapest, P.O. Box 127, Hungary","Dept. of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka, Sinjuku-ku Tokyo 162-8601, Japan","International College of Arts and Sciences Yokohama City University 22-2, Seto, Kanazawa-ku Yokohama, 236-0027, Japan"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Intitute of Mathematics Hungarian Academy of Sciences 1364 Budapest, P.O. Box 127, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Dept. of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka, Sinjuku-ku Tokyo 162-8601, Japan","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"International College of Arts and Sciences Yokohama City University 22-2, Seto, Kanazawa-ku Yokohama, 236-0027, Japan","institution_ids":["https://openalex.org/I89630735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103132798","display_name":"\u00c1gnes N. T\u00f3th","orcid":"https://orcid.org/0000-0003-3218-4724"},"institutions":[{"id":"https://openalex.org/I89630735","display_name":"Yokohama City University","ror":"https://ror.org/0135d1r83","country_code":"JP","type":"education","lineage":["https://openalex.org/I89630735"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU","JP"],"is_corresponding":false,"raw_author_name":"\u00c1gnes T\u00f3th","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Intitute of Mathematics Hungarian Academy of Sciences 1364 Budapest, P.O. Box 127, Hungary","International College of Arts and Sciences Yokohama City University 22-2, Seto, Kanazawa-ku Yokohama, 236-0027, Japan","Dept. of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka, Sinjuku-ku Tokyo 162-8601, Japan"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Intitute of Mathematics Hungarian Academy of Sciences 1364 Budapest, P.O. Box 127, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"raw_affiliation_string":"International College of Arts and Sciences Yokohama City University 22-2, Seto, Kanazawa-ku Yokohama, 236-0027, Japan","institution_ids":["https://openalex.org/I89630735"]},{"raw_affiliation_string":"Dept. of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka, Sinjuku-ku Tokyo 162-8601, Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101970850"],"corresponding_institution_ids":["https://openalex.org/I89630735"],"apc_list":null,"apc_paid":null,"fwci":1.6347,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82324524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9836999773979187,"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/combinatorics","display_name":"Combinatorics","score":0.9127460718154907},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.8638931512832642},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.7814478874206543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7696740627288818},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6931135654449463},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6142751574516296},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5828354358673096},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5283699035644531},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.261019766330719},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18654599785804749}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9127460718154907},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.8638931512832642},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7814478874206543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7696740627288818},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6931135654449463},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6142751574516296},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5828354358673096},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5283699035644531},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.261019766330719},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18654599785804749},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/4137","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4137","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p33/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"}],"best_oa_location":{"id":"doi:10.37236/4137","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4137","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p33/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/G1612663040","display_name":null,"funder_award_id":"108947","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G1615567366","display_name":null,"funder_award_id":"K104343","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G2144793108","display_name":null,"funder_award_id":"104343","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G2256499016","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scientists (","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2983449479","display_name":null,"funder_award_id":"Scientific Research","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3236194794","display_name":null,"funder_award_id":"Grant-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3348058139","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scien","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3459562248","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4367772926","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scientists","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4873009569","display_name":null,"funder_award_id":"Grant-in-Aid for Young Scientists (B)","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4874944895","display_name":null,"funder_award_id":"-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6767705101","display_name":"\u30d4\u30b3\u79d2\u30d1\u30eb\u30b9\u30e9\u30b8\u30aa\u30ea\u30b7\u30b9\u306b\u3088\u308b\u53cd\u5fdc\u4e2d\u9593\u4f53\u306e\u7814\u7a76","funder_award_id":"074009","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6991607394","display_name":null,"funder_award_id":"K108947","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G7022557711","display_name":"\u71b1\u6838\u3068\u95a2\u9023\u3059\u308b\u4f5c\u7528\u7d20\u306e\u7814\u7a76","funder_award_id":"20740095","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7752643416","display_name":null,"funder_award_id":"Japan","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8831030931","display_name":null,"funder_award_id":"108947","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"}],"funders":[{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2160146419.pdf","grobid_xml":"https://content.openalex.org/works/W2160146419.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W156955290","https://openalex.org/W600072479","https://openalex.org/W1826676154","https://openalex.org/W1981383663","https://openalex.org/W2043399762","https://openalex.org/W2057452136"],"related_works":["https://openalex.org/W2509614667","https://openalex.org/W4376608589","https://openalex.org/W2963293152","https://openalex.org/W4302199713","https://openalex.org/W4282026465","https://openalex.org/W3138003926","https://openalex.org/W2988746064","https://openalex.org/W2045621845","https://openalex.org/W2924623028","https://openalex.org/W4288411600"],"abstract_inverted_index":{"For":[0],"$r\\geq":[1],"2$,":[2],"$\\alpha":[3,31],"\\geq":[4],"r-1$":[5],"and":[6,74,104],"$k\\geq":[7],"1$,":[8],"let":[9],"$c(r,\\alpha":[10],",k)$":[11],"be":[12,35],"the":[13,19,45,91],"smallest":[14],"integer":[15],"$c$":[16,38],"such":[17,56],"that":[18,57,82,99],"vertex":[20],"set":[21],"of":[22,48,52,67,78],"any":[23,62,86],"non-trivial":[24],"$r$-uniform":[25],"$k$-edge-colored":[26],"hypergraph":[27],"${\\cal":[28],"H}$":[29],"with":[30],"({\\cal":[32],"H})=\\alpha$":[33],"can":[34],"covered":[36],"by":[37],"monochromatic":[39],"connected":[40],"components.":[41],"Here":[42],"$\\alpha({\\cal{H}})$":[43],"is":[44,69],"maximum":[46],"cardinality":[47],"a":[49,75],"subset":[50],"$A$":[51,58],"vertices":[53],"in":[54],"$\\cal{H}$":[55],"does":[59],"not":[60],"contain":[61],"edges.":[63],"An":[64],"old":[65],"conjecture":[66],"Ryser":[68],"equivalent":[70],"to":[71,94],"$c(2,\\alpha,k)=\\alpha":[72],"(r-1)$":[73],"recent":[76],"result":[77],"Z.":[79],"Kir\u00e1ly":[80],"states":[81],"$c(r,r-1,k)=\\lceil":[83],"\\frac{k}{r}\\rceil$":[84],"for":[85,101,106],"$r\\ge":[87,102,107],"3$.Here":[88],"we":[89],"make":[90],"first":[92],"step":[93],"treat":[95],"non-complete":[96],"hypergraphs,":[97],"showing":[98],"$c(r,r,r)=2$":[100],"2$":[103],"$c(r,r,r+1)=3$":[105],"3$.":[108]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}