{"id":"https://openalex.org/W2172267233","doi":"https://doi.org/10.37236/1542","title":"Inequality Related to Vizing's Conjecture","display_name":"Inequality Related to Vizing's Conjecture","publication_year":2000,"publication_date":"2000-05-24","ids":{"openalex":"https://openalex.org/W2172267233","doi":"https://doi.org/10.37236/1542","mag":"2172267233"},"language":"en","primary_location":{"id":"doi:10.37236/1542","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1542","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1n4/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1n4/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110212458","display_name":"W. Edwin Clark","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":"W. Edwin Clark","raw_affiliation_strings":["Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA","institution_ids":["https://openalex.org/I2613432"]}]},{"author_position":"last","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":false,"raw_author_name":"Stephen Suen","raw_affiliation_strings":["Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA","institution_ids":["https://openalex.org/I2613432"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110212458"],"corresponding_institution_ids":["https://openalex.org/I2613432"],"apc_list":null,"apc_paid":null,"fwci":0.4684,"has_fulltext":true,"cited_by_count":95,"citation_normalized_percentile":{"value":0.70162482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"7","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":0.9987000226974487,"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":0.9987000226974487,"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":0.9785000085830688,"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":0.9585999846458435,"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/mathematics","display_name":"Mathematics","score":0.8923566937446594},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.8804748058319092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8410820960998535},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7196221351623535},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6591478586196899},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.6059664487838745},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.6056491732597351},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5714410543441772},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40029600262641907},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06601506471633911}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8923566937446594},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.8804748058319092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8410820960998535},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7196221351623535},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6591478586196899},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6059664487838745},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.6056491732597351},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5714410543441772},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40029600262641907},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06601506471633911},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1542","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1542","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1n4/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":false,"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:10.1.1.217.6762","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.6762","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/Volume_7/PDF/v7i1n4.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1542","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1542","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1n4/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":false,"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":[{"id":"https://metadata.un.org/sdg/10","score":0.49000000953674316,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2172267233.pdf","grobid_xml":"https://content.openalex.org/works/W2172267233.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1489006728","https://openalex.org/W2003616551","https://openalex.org/W2040458189","https://openalex.org/W2045081006","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W6227737","https://openalex.org/W1588305999","https://openalex.org/W2999514658","https://openalex.org/W2782153997","https://openalex.org/W2383129606","https://openalex.org/W1602143767","https://openalex.org/W2624687997","https://openalex.org/W2611334166","https://openalex.org/W1791282379","https://openalex.org/W2951306406"],"abstract_inverted_index":{"Let":[0],"$\\gamma(G)$":[1],"denote":[2,14],"the":[3,15],"domination":[4],"number":[5],"of":[6,18],"a":[7],"graph":[8],"$G$":[9,20,35],"and":[10,21,36],"let":[11],"$G\\square":[12],"H$":[13],"Cartesian":[16],"product":[17],"graphs":[19,34],"$H$.":[22,37],"We":[23],"prove":[24],"that":[25],"$\\gamma(G)\\gamma(H)":[26],"\\le":[27],"2":[28],"\\gamma(G\\square":[29],"H)$":[30],"for":[31],"all":[32],"simple":[33]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":18}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}