{"title":"立体图形的堆积数","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":50571,"journal":{"name":"Discrete Optimization","volume":"53 ","pages":"Article 100850"},"PeriodicalIF":0.9000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":50571,\"journal\":{\"name\":\"Discrete Optimization\",\"volume\":\"53 \",\"pages\":\"Article 100850\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S157252862400029X\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S157252862400029X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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 .
期刊介绍：
Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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