{"title":"The packing number of cubic graphs","authors":"Wayne Goddard , Michael A. Henning","doi":"10.1016/j.disopt.2024.100850","DOIUrl":null,"url":null,"abstract":"<div><p>A packing in a graph is a set of vertices that are mutually distance at least 3 apart. By using optimization and linear programming to help analyze the greedy algorithm, we improve on a result of Favaron and show that every connected cubic graph of order <span><math><mi>n</mi></math></span> has a packing of size at least <span><math><mrow><mfrac><mrow><mn>17</mn></mrow><mrow><mn>132</mn></mrow></mfrac><mi>n</mi><mo>−</mo><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S157252862400029X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A packing in a graph is a set of vertices that are mutually distance at least 3 apart. By using optimization and linear programming to help analyze the greedy algorithm, we improve on a result of Favaron and show that every connected cubic graph of order has a packing of size at least .
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