{"id":"https://openalex.org/W3165526607","doi":"https://doi.org/10.37236/10453","title":"Independent Sets in Subgraphs of a Shift Graph","display_name":"Independent Sets in Subgraphs of a Shift Graph","publication_year":2022,"publication_date":"2022-02-11","ids":{"openalex":"https://openalex.org/W3165526607","doi":"https://doi.org/10.37236/10453","mag":"3165526607"},"language":"en","primary_location":{"id":"doi:10.37236/10453","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10453","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p26/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":"preprint","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/v29i1p26/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043014235","display_name":"Andrii Arman","orcid":"https://orcid.org/0000-0003-1462-5733"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrii Arman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109078443","display_name":"Vojt\u011bch R\u00f6dl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vojt\u011bch R\u00f6dl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023828026","display_name":"Marcelo Tadeu Sales","orcid":"https://orcid.org/0000-0001-7561-8073"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcelo Tadeu Sales","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043014235"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06047147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"1","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/T10374","display_name":"Advanced Graph Theory Research","score":0.986299991607666,"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/T11476","display_name":"Graph theory and applications","score":0.9793000221252441,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8727210760116577},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.6492105722427368},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6299467086791992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.609071671962738},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.5840550065040588},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36068254709243774}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8727210760116577},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.6492105722427368},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6299467086791992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.609071671962738},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.5840550065040588},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36068254709243774},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10453","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10453","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p26/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:2105.10971","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.10971","pdf_url":"https://arxiv.org/pdf/2105.10971","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"mag:3165526607","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2105.10971.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2105.10971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2105.10971","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"doi:10.37236/10453","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10453","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p26/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/G1664930887","display_name":null,"funder_award_id":"1764385","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5831890411","display_name":null,"funder_award_id":"DMS 1764385","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3165526607.pdf","grobid_xml":"https://content.openalex.org/works/W3165526607.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1781028155","https://openalex.org/W1979578534","https://openalex.org/W1997657048","https://openalex.org/W2161409967","https://openalex.org/W3099835900","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W2749389382","https://openalex.org/W2953087046","https://openalex.org/W2518244851","https://openalex.org/W2992307599","https://openalex.org/W2146066930","https://openalex.org/W2912124299","https://openalex.org/W2783285849","https://openalex.org/W3172394114","https://openalex.org/W3049219688","https://openalex.org/W2950553327","https://openalex.org/W3210829833","https://openalex.org/W2004627446","https://openalex.org/W3098406359","https://openalex.org/W2576540604","https://openalex.org/W3177473685","https://openalex.org/W3165892239","https://openalex.org/W3033800685","https://openalex.org/W3120344684","https://openalex.org/W3209002032","https://openalex.org/W2952877655"],"abstract_inverted_index":{"Erd\u0151s,":[0],"Hajnal":[1],"and":[2,46,58],"Szemer\u00e9di":[3],"proved":[4],"that":[5,19,43],"any":[6],"subset":[7],"$G$":[8,28],"of":[9,11,23],"vertices":[10],"a":[12,66],"shift":[13,71],"graph":[14],"$\\text{Sh}_{n}^{k}$":[15],"has":[16],"the":[17,20,24],"property":[18],"independence":[21],"number":[22],"subgraph":[25],"induced":[26],"by":[27],"satisfies":[29],"$\\alpha(\\text{Sh}_{n}^{k}[G])\\geq":[30],"\\left(\\frac{1}{2}-\\varepsilon\\right)|G|$,":[31],"where":[32],"$\\varepsilon\\to":[33],"0$":[34],"as":[35],"$k\\to":[36],"\\infty$.":[37],"In":[38],"this":[39],"note":[40],"we":[41],"prove":[42],"for":[44,69],"$k=2$":[45],"$n":[47],"\\to":[48],"\\infty$":[49],"there":[50],"are":[51],"graphs":[52],"$G\\subseteq":[53],"\\binom{[n]}{2}$":[54],"with":[55],"$\\alpha(\\text{Sh}_{n}^{2}[G])\\leq":[56],"\\left(\\frac{1}{4}+o(1)\\right)|G|$,":[57],"$\\frac{1}{4}$":[59],"is":[60],"best":[61],"possible.":[62],"We":[63],"also":[64],"consider":[65],"related":[67],"problem":[68],"infinite":[70],"graphs.":[72]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}