{"title":"New bounds on a hypercube coloring problem and linear codes","authors":"H. Q. Ngo, D. Du, R. Graham","doi":"10.1109/ITCC.2001.918853","DOIUrl":null,"url":null,"abstract":"In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of /spl chi//sub k~/(n), the minimum number of colors needed, appears to be a difficult problem. We improve the known lower and upper bounds of /spl chi//sub k~/(n) and indicate the connection of this colouring problem to linear codes.","PeriodicalId":318295,"journal":{"name":"Proceedings International Conference on Information Technology: Coding and Computing","volume":"19 4","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings International Conference on Information Technology: Coding and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITCC.2001.918853","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of /spl chi//sub k~/(n), the minimum number of colors needed, appears to be a difficult problem. We improve the known lower and upper bounds of /spl chi//sub k~/(n) and indicate the connection of this colouring problem to linear codes.