{"id":"https://openalex.org/W7213277102","doi":"https://doi.org/10.48550/arxiv.2609.14655","title":"Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko","display_name":"Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213277102","doi":"https://doi.org/10.48550/arxiv.2609.14655"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14655","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14655","pdf_url":"https://arxiv.org/pdf/2609.14655","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/2609.14655","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151825921","display_name":"Hao Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113292033","display_name":"Yupeng Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin, Yupeng","raw_affiliation_strings":["School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"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":1.0,"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":0.0,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"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/oriented-paths","display_name":"oriented paths","score":0.8209999799728394},{"id":"https://openalex.org/keywords/homomorphism-densities","display_name":"homomorphism densities","score":0.9819999933242798},{"id":"https://openalex.org/keywords/tournaments","display_name":"tournaments","score":0.6119999885559082},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.7129999995231628}],"concepts":[{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.9503999948501587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7443000078201294},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6495000123977661},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5874999761581421},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.413100004196167},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.2702000141143799},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14655","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14655","pdf_url":"https://arxiv.org/pdf/2609.14655","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.2609.14655","doi":"https://doi.org/10.48550/arxiv.2609.14655","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14655","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:2609.14655","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14655","pdf_url":"https://arxiv.org/pdf/2609.14655","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":[{"id":"https://openalex.org/G1330075977","display_name":null,"funder_award_id":"12125106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1836446064","display_name":null,"funder_award_id":"12125106","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G442152759","display_name":null,"funder_award_id":"2023YFA1010201","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213277102.pdf","grobid_xml":"https://content.openalex.org/works/W7213277102.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4391833844","https://openalex.org/W7115591989","https://openalex.org/W7129049055","https://openalex.org/W7161268947"],"related_works":["https://openalex.org/W7161268947","https://openalex.org/W7115591989","https://openalex.org/W3120076571","https://openalex.org/W7095528523","https://openalex.org/W4391833844","https://openalex.org/W4415069644","https://openalex.org/W2026936073","https://openalex.org/W2030414567","https://openalex.org/W7171534754","https://openalex.org/W2804154168"],"abstract_inverted_index":{"An":[0],"oriented":[1,28,69,109],"graph":[2],"$H$":[3,22],"is":[4,34,79,120],"said":[5],"to":[6,89],"be":[7],"tournament":[8,15,121],"anti-Sidorenko":[9],"(TAS)":[10],"if":[11],"a":[12,31,35],"uniformly":[13],"random":[14],"asymptotically":[16],"maximizes":[17],"the":[18],"homomorphism":[19],"density":[20],"of":[21,71,111],"among":[23],"all":[24],"tournaments.":[25],"For":[26],"an":[27],"path":[29,70,110],"$P$,":[30],"direction":[32,52,77,118],"flip":[33,78],"non-leaf":[36],"source":[37],"or":[38],"sink.":[39],"Sah,":[40],"Sawhney":[41],"and":[42,60,81,84],"Zhao":[43],"proved":[44,62],"that":[45,63,102],"consistently":[46],"directed":[47],"paths":[48],"(paths":[49],"with":[50,74,116],"no":[51],"flips)":[53],"are":[54],"TAS.":[55],"He,":[56],"Mani,":[57],"Nie,":[58],"Tung":[59],"Wei":[61],"for":[64,103],"$3\\le":[65],"k\\le":[66],"7$,":[67],"every":[68,90,104,108],"length":[72,112],"$k$":[73],"exactly":[75],"one":[76],"TAS,":[80],"Chen,":[82],"Clemen":[83],"Noel":[85],"recently":[86],"extended":[87],"this":[88,94],"$k\\ge":[91],"3$.":[92],"In":[93],"paper,":[95],"we":[96],"extend":[97],"these":[98],"results":[99],"by":[100],"proving":[101],"integer":[105],"$r\\ge":[106],"0$,":[107],"at":[113],"least":[114],"$1665r+1454$":[115],"$r$":[117],"flips":[119],"anti-Sidorenko.":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
