{"id":"https://openalex.org/W7223044760","doi":"https://doi.org/10.48550/arxiv.2610.25817","title":"The multiplicative Merino--Welsh inequality for chordal graphs","display_name":"The multiplicative Merino--Welsh inequality for chordal graphs","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223044760","doi":"https://doi.org/10.48550/arxiv.2610.25817"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.25817","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25817","pdf_url":"https://arxiv.org/pdf/2610.25817","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/2610.25817","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159095299","display_name":"Shaohan Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Shaohan","raw_affiliation_strings":["MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles , Nanjing , Jiangsu , 210016 , PR China","School of Mathematics , Nanjing University of Aeronautics and Astronautics , Nanjing , Jiangsu , 210016 , PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles , Nanjing , Jiangsu , 210016 , PR China","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics , Nanjing University of Aeronautics and Astronautics , Nanjing , Jiangsu , 210016 , PR China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040286132","display_name":"Fengming Dong","orcid":"https://orcid.org/0000-0002-8510-2262","observed_orcids":["https://orcid.org/0000-0002-8510-2262"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dong, Fengming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159103175","display_name":"Kexiang Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Kexiang","raw_affiliation_strings":["MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles , Nanjing , Jiangsu , 210016 , PR China","School of Mathematics , Nanjing University of Aeronautics and Astronautics , Nanjing , Jiangsu , 210016 , PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles , Nanjing , Jiangsu , 210016 , PR China","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics , Nanjing University of Aeronautics and Astronautics , Nanjing , Jiangsu , 210016 , PR China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.6079000234603882,"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":0.6079000234603882,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.23929999768733978,"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":0.12049999833106995,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-inequalities","display_name":"multiplicative inequalities","score":0.7269999980926514},{"id":"https://openalex.org/keywords/chordal-graphs","display_name":"chordal graphs","score":0.9599999785423279},{"id":"https://openalex.org/keywords/bridgeless-graphs","display_name":"bridgeless graphs","score":0.8149999976158142},{"id":"https://openalex.org/keywords/spanning-trees","display_name":"spanning trees","score":0.9679999947547913},{"id":"https://openalex.org/keywords/acyclic-orientations","display_name":"acyclic orientations","score":0.996999979019165},{"id":"https://openalex.org/keywords/graph-invariants","display_name":"graph invariants","score":0.49300000071525574}],"concepts":[{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.8098000288009644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7983999848365784},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7595999836921692},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6071000099182129},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.5817999839782715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5449000000953674},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.3871999979019165},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.3571999967098236},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.30059999227523804},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.25817","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25817","pdf_url":"https://arxiv.org/pdf/2610.25817","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.2610.25817","doi":"https://doi.org/10.48550/arxiv.2610.25817","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25817","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:2610.25817","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25817","pdf_url":"https://arxiv.org/pdf/2610.25817","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":[{"id":"https://openalex.org/G8803877644","display_name":null,"funder_award_id":"12271251","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223044760.pdf","grobid_xml":"https://content.openalex.org/works/W7223044760.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7214773041"],"related_works":["https://openalex.org/W2319153776","https://openalex.org/W2141380527","https://openalex.org/W2002787104","https://openalex.org/W2315377764","https://openalex.org/W76296007","https://openalex.org/W2594595227","https://openalex.org/W2391016997","https://openalex.org/W7097219232","https://openalex.org/W4229005845","https://openalex.org/W7124258042"],"abstract_inverted_index":{"For":[0],"a":[1],"connected":[2,29],"graph":[3],"$G$,":[4],"let":[5],"$\u03c4(G)$,":[6],"$\u03b1(G)$":[7],"and":[8,18],"$\u03b1^*(G)$":[9],"denote":[10],"its":[11],"numbers":[12],"of":[13],"spanning":[14],"trees,":[15],"acyclic":[16],"orientations":[17],"totally":[19],"cyclic":[20],"orientations,":[21],"respectively.":[22],"We":[23],"prove":[24],"that":[25],"$\u03b1(G)\u03b1^*(G)\\geq\u03c4(G)^2$":[26],"for":[27],"every":[28],"bridgeless":[30],"chordal":[31],"graph.":[32]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
