{"id":"https://openalex.org/W7147207017","doi":"https://doi.org/10.48550/arxiv.2603.29629","title":"On graph products and multi-word-representability","display_name":"On graph products and multi-word-representability","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7147207017","doi":"https://doi.org/10.48550/arxiv.2603.29629"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.29629","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29629","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.29629","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083886435","display_name":"Benny George Kenkireth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kenkireth, Benny George","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132684424","display_name":"Gopalan Sajith","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sajith, Gopalan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5116248542","display_name":"Sreyas Sasidharan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sasidharan, Sreyas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.6718000173568726,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.6718000173568726,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.15049999952316284,"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/T11476","display_name":"Graph theory and applications","score":0.050599999725818634,"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/lexicographical-order","display_name":"Lexicographical order","score":0.9728000164031982},{"id":"https://openalex.org/keywords/comparability","display_name":"Comparability","score":0.8901000022888184},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.588100016117096},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5194000005722046},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4034000039100647}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.9728000164031982},{"id":"https://openalex.org/C197947376","wikidata":"https://www.wikidata.org/wiki/Q5155608","display_name":"Comparability","level":2,"score":0.8901000022888184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512999773025513},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.588100016117096},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5252000093460083},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5194000005722046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43529999256134033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.257999986410141}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.29629","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29629","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.29629","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29629","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"multi-word-representation":[1],"number":[2,11,165],"$\u03bc(G)$":[3],"of":[4,12,23,103,166,213],"a":[5,67,88,152,181,189,209],"graph":[6,28,207],"$G$":[7,147,179],"is":[8,17,148,159,173,180],"the":[9,21,30,40,54,74,97,100,111,124,162,194,200],"minimum":[10],"word-representable":[13,149,174,210],"graphs":[14,107],"whose":[15],"union":[16],"$G$.":[18,167],"We":[19,168],"study":[20],"behavior":[22],"$\u03bc$":[24],"under":[25,69,87],"six":[26],"standard":[27],"products:":[29],"lexicographic,":[31],"Cartesian,":[32],"rooted,":[33],"corona,":[34],"tensor,":[35],"and":[36,42,64,94,155,176],"strong":[37,125],"products.":[38],"For":[39,53,73,110,123,137],"Cartesian":[41],"rooted":[43],"products,":[44],"we":[45,57,65,77,95,117,130,141,187],"show":[46,118,170],"that":[47,59,143,171,204,214],"$\u03bc(G_1":[48,60,79,119],"\\square":[49],"G_2)=\u03bc(G_1":[50],"\\diamond":[51],"G_2)=\\max\\{\u03bc(G_1),\u03bc(G_2)\\}$.":[52],"corona":[55],"product,":[56,76],"prove":[58,142],"\\odot":[61],"G_2)\\le":[62,81,121,135],"\\max\\{\u03bc(G_1),\u03bc(G_2)\\}+1$,":[63],"identify":[66],"condition":[68,91],"which":[70,83],"equality":[71],"holds.":[72],"lexicographic":[75,101,138],"establish":[78,131],"\\circ":[80],"\u03bc(G_1)+\u03bc(G_2)$,":[82],"reduces":[84],"to":[85],"$\\max\\{\u03bc(G_1),\u03bc(G_2)\\}$":[86],"comparability":[89,153,163,182],"cover":[90,164],"on":[92,193],"$G_2$,":[93],"characterize":[96],"case":[98],"when":[99,146],"product":[102,113,126],"two":[104],"minimal":[105],"non-word-representable":[106],"has":[108],"$\u03bc=2$.":[109],"tensor":[112],"$G_1":[114,127],"\\times":[115,120],"G_2$,":[116,129],"\\log_3(\\min\\{\u03c7(G_1),\u03c7(G_2)\\})$.":[122],"\\boxtimes":[128,134],"$\\max\\{\u03bc(G_1),\u03bc(G_2)\\}\\le":[132],"\u03bc(G_1":[133],"\\max\\{\u03bc(G_1),\u03bc(G_2)\\}+\\log_3(\\min\\{\u03c7(G_1),\u03c7(G_2)\\})$.":[136],"powers":[139],"$G^{[k]}$,":[140],"$\u03bc(G^{[k]})\\le":[144],"k$":[145],"but":[150],"not":[151],"graph,":[154],"in":[156,216],"general":[157],"$\u03bc(G^{[k]})$":[158],"bounded":[160],"by":[161],"further":[169],"$G^{[k]}$":[172],"if":[175,178],"only":[177],"graph.":[183],"As":[184],"an":[185],"application,":[186],"obtain":[188],"sublinear":[190],"upper":[191],"bound":[192],"extremal":[195],"function":[196],"$\u03c4(n)$,":[197],"defined":[198],"as":[199],"largest":[201],"integer":[202],"such":[203],"every":[205],"$n$-vertex":[206],"contains":[208],"induced":[211],"subgraph":[212],"size;":[215],"particular,":[217],"$\u03c4(8^k)\\le":[218],"6^k$,":[219],"implying":[220],"$\u03c4(n)\\le":[221],"n^{\\log_8":[222],"6+\u03b5}$":[223],"for":[224],"large":[225],"$n$.":[226]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-02T00:00:00"}
