{"id":"https://openalex.org/W1565712860","doi":"https://doi.org/10.37236/15","title":"An Improved Inequality Related to Vizing's Conjecture","display_name":"An Improved Inequality Related to Vizing's Conjecture","publication_year":2012,"publication_date":"2012-01-06","ids":{"openalex":"https://openalex.org/W1565712860","doi":"https://doi.org/10.37236/15","mag":"1565712860"},"language":"en","primary_location":{"id":"doi:10.37236/15","is_oa":true,"landing_page_url":"https://doi.org/10.37236/15","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p8/pdf","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":null,"license_id":null,"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://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p8/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082619047","display_name":"Stephen Suen","orcid":null},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephen Suen","raw_affiliation_strings":["University of South Florida","University of South FLorida"],"affiliations":[{"raw_affiliation_string":"University of South Florida","institution_ids":["https://openalex.org/I2613432"]},{"raw_affiliation_string":"University of South FLorida","institution_ids":["https://openalex.org/I2613432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071937643","display_name":"Jennifer M Tarr","orcid":null},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jennifer Tarr","raw_affiliation_strings":["University of South Florida","University of South FLorida"],"affiliations":[{"raw_affiliation_string":"University of South Florida","institution_ids":["https://openalex.org/I2613432"]},{"raw_affiliation_string":"University of South FLorida","institution_ids":["https://openalex.org/I2613432"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082619047"],"corresponding_institution_ids":["https://openalex.org/I2613432"],"apc_list":null,"apc_paid":null,"fwci":2.7643,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.89948711,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"1","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":0.9952999949455261,"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":0.9952999949455261,"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/T11476","display_name":"Graph theory and applications","score":0.9940000176429749,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9912999868392944,"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/conjecture","display_name":"Conjecture","score":0.8910149335861206},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8366541862487793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8105432391166687},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6430563926696777},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5777994394302368},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.43100011348724365},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3758729100227356}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8910149335861206},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8366541862487793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8105432391166687},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6430563926696777},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5777994394302368},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.43100011348724365},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3758729100227356},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"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":2,"locations":[{"id":"doi:10.37236/15","is_oa":true,"landing_page_url":"https://doi.org/10.37236/15","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p8/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.369.5193","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.5193","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v19i1p8/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/15","is_oa":true,"landing_page_url":"https://doi.org/10.37236/15","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p8/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1565712860.pdf","grobid_xml":"https://content.openalex.org/works/W1565712860.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1990941137","https://openalex.org/W2172267233"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4291318508","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W2794522194","https://openalex.org/W2349109195","https://openalex.org/W2069797780","https://openalex.org/W4297965885","https://openalex.org/W2078360221"],"abstract_inverted_index":{"Vizing":[0],"conjectured":[1,27],"in":[2,59],"1963":[3],"that":[4,62],"$\\gamma(G":[5,63],"\\Box":[6,64],"H)":[7,65],"\\geq":[8,66],"\\gamma(G)\\gamma(H)$":[9],"for":[10,30,41,51,68],"any":[11,33,69],"graphs":[12,70],"$G$":[13,18,31,71],"and":[14,32,45,57,72],"$H$.":[15,35,73],"A":[16],"graph":[17,34],"is":[19,47],"said":[20],"to":[21,49],"satisfy":[22],"Vizing's":[23,36],"conjecture":[24,37],"if":[25],"the":[26],"inequality":[28,81],"holds":[29],"has":[38],"been":[39],"proved":[40],"$\\gamma(G)":[42],"\\le":[43],"3$,":[44],"it":[46],"known":[48],"hold":[50],"other":[52],"classes":[53],"of":[54,79],"graphs.":[55],"Clark":[56],"Suen":[58],"2000":[60],"showed":[61],"\\frac{1}{2}\\gamma(G)\\gamma(H)$":[67],"We":[74],"give":[75],"a":[76],"slight":[77],"improvement":[78],"this":[80],"by":[82],"tightening":[83],"their":[84],"arguments.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
