{"id":"https://openalex.org/W2964218640","doi":"https://doi.org/10.37236/6885","title":"Maximum Size of a Family of Pairwise Graph-Different Permutations","display_name":"Maximum Size of a Family of Pairwise Graph-Different Permutations","publication_year":2017,"publication_date":"2017-10-20","ids":{"openalex":"https://openalex.org/W2964218640","doi":"https://doi.org/10.37236/6885","mag":"2964218640"},"language":"en","primary_location":{"id":"doi:10.37236/6885","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6885","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/10.37236/6885","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050779105","display_name":"Louis Golowich","orcid":"https://orcid.org/0000-0002-5169-0596"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Louis Golowich","raw_affiliation_strings":["MIT PRIMES"],"affiliations":[{"raw_affiliation_string":"MIT PRIMES","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065495152","display_name":"Chiheon Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Chiheon Kim","raw_affiliation_strings":["MIT","-MIT"],"affiliations":[{"raw_affiliation_string":"MIT","institution_ids":["https://openalex.org/I4210109586"]},{"raw_affiliation_string":"-MIT","institution_ids":["https://openalex.org/I4210109586"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007748704","display_name":"Richard Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Zhou","raw_affiliation_strings":["MIT PRIMES"],"affiliations":[{"raw_affiliation_string":"MIT PRIMES","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050779105"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5007,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65145665,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"4","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":0.996399998664856,"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":0.996399998664856,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9617999792098999,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9296000003814697,"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":0.9266830086708069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8305292129516602},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5682064294815063},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5404272079467773},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49085551500320435},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4422770142555237},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.4403376579284668},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4299105703830719},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42109352350234985},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06084933876991272},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05282941460609436}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9266830086708069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8305292129516602},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5682064294815063},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5404272079467773},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49085551500320435},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4422770142555237},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.4403376579284668},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4299105703830719},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42109352350234985},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06084933876991272},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05282941460609436},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6885","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6885","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"}],"best_oa_location":{"id":"doi:10.37236/6885","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6885","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/W2020053772","https://openalex.org/W2035433397","https://openalex.org/W2132137594","https://openalex.org/W2069783012","https://openalex.org/W2085967955","https://openalex.org/W4256335355","https://openalex.org/W3098612666","https://openalex.org/W1499116563","https://openalex.org/W2138867060","https://openalex.org/W2023859141"],"abstract_inverted_index":{"Two":[0],"permutations":[1,25,44,73,113],"of":[2,5,22,38,41,58,70,74,77,85,102,107,110,118,135,151,154],"the":[3,23,35,67,75,100,104,133,152],"vertices":[4,76,120],"a":[6,39,108,124],"graph":[7,134],"$G$":[8,57,78,88],"are":[9],"called":[10],"$G$-different":[11,43,72],"if":[12],"there":[13],"exists":[14],"an":[15,27,115],"index":[16],"$i$":[17],"such":[18],"that":[19,51,94],"$i$-th":[20],"entry":[21],"two":[24],"form":[26],"edge":[28],"in":[29],"$G$.":[30,48],"We":[31,49,81,98,127],"bound":[32],"or":[33],"determine":[34,128],"maximum":[36,68,90,105],"size":[37,106],"family":[40,109],"pairwise":[42,71,111],"for":[45,52,132,148],"various":[46],"graphs":[47,56,87,149],"show":[50],"all":[53],"balanced":[54],"bipartite":[55,86],"order":[59],"$n$":[60],"with":[61,89],"minimum":[62],"degree":[63,91],"$n/2":[64],"-":[65],"o(n)$,":[66],"number":[69,117],"is":[79,121],"$2^{(1-o(1))n}$.":[80],"also":[82],"present":[83,140],"examples":[84],"$O(\\log":[92],"n)$":[93],"have":[95],"this":[96,129,146],"property.":[97],"explore":[99],"problem":[101],"bounding":[103],"graph-different":[112],"when":[114],"unlimited":[116],"disjoint":[119,137,156],"added":[122],"to":[123,145],"given":[125],"graph.":[126],"exact":[130],"value":[131,147],"2":[136],"edges,":[138],"and":[139],"some":[141],"asymptotic":[142],"bounds":[143],"relating":[144],"consisting":[150],"union":[153],"$n/2$":[155],"edges.":[157]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}