{"id":"https://openalex.org/W2611415465","doi":"https://doi.org/10.37236/5954","title":"On the Caccetta-H\u00e4ggkvist Conjecture with a Forbidden Transitive Tournament","display_name":"On the Caccetta-H\u00e4ggkvist Conjecture with a Forbidden Transitive Tournament","publication_year":2017,"publication_date":"2017-05-05","ids":{"openalex":"https://openalex.org/W2611415465","doi":"https://doi.org/10.37236/5954","mag":"2611415465"},"language":"en","primary_location":{"id":"doi:10.37236/5954","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5954","pdf_url":null,"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://doi.org/10.37236/5954","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034742583","display_name":"Andrzej Grzesik","orcid":"https://orcid.org/0000-0003-2770-7180"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Andrzej Grzesik","raw_affiliation_strings":["Faculty of Mathematics and Computer Science,\r\nJagiellonian University,\r\nul. St. \u0141ojasiewicza 6,\r\n30-348 Krak\u00f3w, Poland","Faculty of Mathematics and Computer Science,\nJagiellonian University,\nul. St. \u0141ojasiewicza 6,\n30-348 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science,\r\nJagiellonian University,\r\nul. St. \u0141ojasiewicza 6,\r\n30-348 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science,\nJagiellonian University,\nul. St. \u0141ojasiewicza 6,\n30-348 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034742583"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":null,"apc_paid":null,"fwci":0.844,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70134648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9959999918937683,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9959999918937683,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9951000213623047,"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/T11567","display_name":"semigroups and automata theory","score":0.9936000108718872,"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/tournament","display_name":"Tournament","score":0.9096143841743469},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9095290899276733},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8589401245117188},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8339274525642395},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.5995169878005981},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5240473747253418},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5137253999710083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4506082236766815}],"concepts":[{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.9096143841743469},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9095290899276733},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8589401245117188},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8339274525642395},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.5995169878005981},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5240473747253418},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5137253999710083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4506082236766815}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/5954","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5954","pdf_url":null,"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:ruj.uj.edu.pl:item/40460","is_oa":false,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/40460","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","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":"artyku\u0142 w czasopi\u015bmie"}],"best_oa_location":{"id":"doi:10.37236/5954","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5954","pdf_url":null,"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3123786980","https://openalex.org/W4287997709","https://openalex.org/W2994965880","https://openalex.org/W3083287393","https://openalex.org/W2044692892","https://openalex.org/W3103832149","https://openalex.org/W2911409521","https://openalex.org/W4288416186","https://openalex.org/W981035018","https://openalex.org/W2771742342"],"abstract_inverted_index":{"The":[0,71],"Caccetta-H\u00e4ggkvist":[1,55,124],"Conjecture":[2,56,125],"asserts":[3],"that":[4,53,80,142],"every":[5],"oriented":[6],"graph":[7,145,168],"on":[8,41,48,135,159],"$n$":[9],"vertices":[10,161],"without":[11,131],"directed":[12,157],"cycles":[13],"of":[14,74,85,99,122,129,155,182],"length":[15],"less":[16],"than":[17],"or":[18],"equal":[19],"to":[20,151],"$l$":[21],"has":[22,150],"minimum":[23,49],"outdegree":[24],"at":[25],"most":[26,117],"$(n-1)/l$.":[27],"In":[28,112],"this":[29,76],"paper":[30],"we":[31],"state":[32],"a":[33,38,45,153,156],"conjecture":[34,61,78,101],"for":[35,66,102,146,169],"graphs":[36,88,130],"missing":[37],"transitive":[39,133],"tournament":[40,134],"$2^k+1$":[42],"vertices,":[43],"with":[44],"weaker":[46],"assumption":[47],"outdegree.":[50],"We":[51],"prove":[52,95],"the":[54,59,83,86,96,100,108,116,123,127,132,143,147,170,179,183],"follows":[57],"from":[58],"presented":[60],"and":[62,69,89,104,119],"show":[63],"matching":[64],"constructions":[65],"all":[67],"$k$":[68],"$l$.":[70],"main":[72],"advantage":[73],"considering":[75],"generalized":[77],"is":[79,139],"it":[81,114],"reduces":[82],"set":[84],"extremal":[87,144,167,184],"allows":[90],"using":[91,107],"an":[92,166],"induction.We":[93],"also":[94,140],"triangle":[97],"case":[98,121,148,171],"$k=1$":[103,172],"$2$":[105],"by":[106],"Razborov's":[109],"flag":[110],"algebras.":[111],"particular,":[113],"proves":[115],"interesting":[118],"studied":[120],"in":[126,163],"class":[128],"5":[136],"vertices.":[137],"It":[138],"shown":[141],"$k=2$":[149],"be":[152],"blow-up":[154],"cycle":[158],"4":[160],"having":[162],"each":[164],"blob":[165],"(complete":[173],"regular":[174],"bipartite":[175],"graph),":[176],"which":[177],"confirms":[178],"conjectured":[180],"structure":[181],"examples.":[185]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
