{"id":"https://openalex.org/W2742577056","doi":"https://doi.org/10.37236/7206","title":"Improved Bounds for the Graham-Pollak Problem for Hypergraphs","display_name":"Improved Bounds for the Graham-Pollak Problem for Hypergraphs","publication_year":2018,"publication_date":"2018-01-12","ids":{"openalex":"https://openalex.org/W2742577056","doi":"https://doi.org/10.37236/7206","mag":"2742577056"},"language":"en","primary_location":{"id":"doi:10.37236/7206","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7206","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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/7206","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050380592","display_name":"Imre Leader","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Imre Leader","raw_affiliation_strings":["University of Cambridge","Univ. of Cambridge"],"affiliations":[{"raw_affiliation_string":"University of Cambridge","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060371759","display_name":"Ta Sheng Tan","orcid":"https://orcid.org/0000-0002-5739-3242"},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Ta Sheng Tan","raw_affiliation_strings":["University of Malaya","University\u200b \u200b of\u200b \u200b Malaya;"],"affiliations":[{"raw_affiliation_string":"University of Malaya","institution_ids":["https://openalex.org/I33849332"]},{"raw_affiliation_string":"University\u200b \u200b of\u200b \u200b Malaya;","institution_ids":["https://openalex.org/I33849332"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050380592"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":0.61471862,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54000659,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9973000288009644,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8524507284164429},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7377506494522095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6385573148727417},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.547573447227478},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3994499146938324}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8524507284164429},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7377506494522095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6385573148727417},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.547573447227478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3994499146938324}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/7206","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7206","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:arXiv.org:1708.01898","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.01898","pdf_url":"https://arxiv.org/pdf/1708.01898","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:2742577056","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1708.01898.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":"pmh:oai:eprints.um.edu.my:21540","is_oa":false,"landing_page_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p4/pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400330","display_name":"The University of Malaya Research Repository (University of Malaya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I33849332","host_organization_name":"University of Malaya","host_organization_lineage":["https://openalex.org/I33849332"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1708.01898","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1708.01898","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:10.37236/7206","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7206","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":9,"referenced_works":["https://openalex.org/W1522673698","https://openalex.org/W1964610196","https://openalex.org/W1967237366","https://openalex.org/W1977325698","https://openalex.org/W1985908622","https://openalex.org/W2036811773","https://openalex.org/W2053898220","https://openalex.org/W2584968584","https://openalex.org/W2785506964"],"related_works":["https://openalex.org/W2963617211","https://openalex.org/W2963886183","https://openalex.org/W2952059987","https://openalex.org/W2903071204","https://openalex.org/W3122344457","https://openalex.org/W2205584677","https://openalex.org/W2395406898","https://openalex.org/W2071732668","https://openalex.org/W2112386335","https://openalex.org/W2742585815","https://openalex.org/W1577085578","https://openalex.org/W1974938276","https://openalex.org/W1993446652","https://openalex.org/W3102068398","https://openalex.org/W3040391339","https://openalex.org/W2884541885","https://openalex.org/W3088736520","https://openalex.org/W2794641614","https://openalex.org/W3197553455","https://openalex.org/W2964269433"],"abstract_inverted_index":{"For":[0],"a":[1],"fixed":[2],"$r$,":[3],"let":[4],"$f_r(n)$":[5],"denote":[6],"the":[7,17,44],"minimum":[8],"number":[9,46],"of":[10,76],"complete":[11,18],"$r$-partite":[12],"$r$-graphs":[13],"needed":[14],"to":[15],"partition":[16],"$r$-graph":[19],"on":[20],"$n$":[21],"vertices.":[22],"The":[23],"Graham-Pollak":[24],"theorem":[25],"asserts":[26],"that":[27,33,48,57,84,90],"$f_2(n)=n-1$.":[28],"An":[29],"easy":[30],"construction":[31],"shows":[32,89],"$f_r(n)":[34,49],"\\leq":[35,50],"(1+o(1))\\binom{n}{\\lfloor":[36,52],"r/2":[37,53],"\\rfloor}$,":[38],"and":[39],"we":[40,82],"write":[41],"$c_r$":[42],"for":[43,61,72],"least":[45],"such":[47],"c_r":[51],"\\rfloor}$.It":[54],"was":[55,69],"known":[56,71],"$c_r":[58,91],"<":[59],"1$":[60],"each":[62],"even":[63],"$r":[64],"\\geq":[65],"4$,":[66],"but":[67],"this":[68,79],"not":[70],"any":[73],"odd":[74],"value":[75],"$r$.":[77],"In":[78],"short":[80],"note,":[81],"prove":[83],"$c_{295}<1$.":[85],"Our":[86],"method":[87],"also":[88],"\\rightarrow":[92],"0$,":[93],"answering":[94],"another":[95],"open":[96],"problem.":[97]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}