{"id":"https://openalex.org/W7213585200","doi":"https://doi.org/10.48550/arxiv.2609.20025","title":"Improved Bounds on the Szeged-Wiener Gap and the BKLPS Conjecture","display_name":"Improved Bounds on the Szeged-Wiener Gap and the BKLPS Conjecture","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213585200","doi":"https://doi.org/10.48550/arxiv.2609.20025"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20025","pdf_url":"https://arxiv.org/pdf/2609.20025","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/2609.20025","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144367873","display_name":"Lily Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhang, Lily","raw_affiliation_strings":["University of California , Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152121928","display_name":"Evan Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li, Evan","raw_affiliation_strings":["University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"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/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.0006000000284984708,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.00019999999494757503,"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/wiener-index","display_name":"Wiener index","score":0.8659999966621399},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.8550000190734863},{"id":"https://openalex.org/keywords/biconnected-graphs","display_name":"2-connected graphs","score":0.8259999752044678},{"id":"https://openalex.org/keywords/complete-graphs","display_name":"complete graphs","score":0.5189999938011169},{"id":"https://openalex.org/keywords/extremal-graphs","display_name":"extremal graphs","score":0.6349999904632568},{"id":"https://openalex.org/keywords/graph-invariants","display_name":"graph invariants","score":0.41200000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.784500002861023},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7788000106811523},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7479000091552734},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5511999726295471},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5349000096321106},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4966000020503998},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.45579999685287476},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C2994516854","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Finite graph","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20025","pdf_url":"https://arxiv.org/pdf/2609.20025","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.2609.20025","doi":"https://doi.org/10.48550/arxiv.2609.20025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20025","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:2609.20025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20025","pdf_url":"https://arxiv.org/pdf/2609.20025","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213585200.pdf","grobid_xml":"https://content.openalex.org/works/W7213585200.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1974345530","https://openalex.org/W2028218608","https://openalex.org/W2032040845","https://openalex.org/W2059603959","https://openalex.org/W2278761997","https://openalex.org/W2318794083"],"related_works":["https://openalex.org/W7214944592","https://openalex.org/W2736271172","https://openalex.org/W2059603959","https://openalex.org/W2994769172","https://openalex.org/W1565712860","https://openalex.org/W2389689074","https://openalex.org/W2963942939","https://openalex.org/W2031573311","https://openalex.org/W2005741846","https://openalex.org/W7135201930"],"abstract_inverted_index":{"Bonamy-Knor-Lu\u017ear-Pinlou-\u0160krekovski":[0],"(2017)":[1],"define":[2],"$K_n^t$":[3],"to":[4,19,50,70,80,105],"be":[5],"the":[6,23,56,72,75,85],"complete":[7,24],"graph":[8,25,42],"of":[9,22,43,59],"$n-1$":[10],"vertices":[11,21],"but":[12],"with":[13],"an":[14],"extra":[15],"vertex":[16],"that's":[17],"adjacent":[18],"$t$":[20],"part.":[26],"They":[27],"propose":[28],"a":[29,38,100,107],"stronger":[30],"conjecture":[31,83],"which":[32],"asserts":[33],"that":[34],"if":[35],"$G$":[36,60],"is":[37,61],"finite":[39],"simple":[40],"$2$-connected":[41],"order":[44],"$n":[45,95],"\\ge":[46,63,96],"10$":[47,97],"not":[48],"isomorphic":[49],"$K_n$,":[51],"$K_n^2$,":[52],"nor":[53],"$K_n^{n-2}$,":[54],"then":[55],"Szeged-Wiener":[57,76],"gap":[58],"$\u03b7(G)":[62],"2n$.":[64],"We":[65],"improve":[66],"upon":[67],"their":[68],"work":[69],"tighten":[71],"bounds":[73],"on":[74],"gap,":[77],"allowing":[78],"us":[79],"prove":[81],"this":[82],"in":[84],"affirmative.":[86],"Afterwards,":[87],"we":[88],"construct":[89],"graphs":[90],"attaining":[91],"equality":[92],"for":[93,102,112],"each":[94],"and":[98,109],"pose":[99],"problem":[101],"interested":[103],"readers":[104],"determine":[106],"necessary":[108],"sufficient":[110],"condition":[111],"equality.":[113]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}