{"title":"Quantum chromatic numbers of products of quantum graphs","authors":"Rolando de Santiago, A. Meenakshi McNamara","doi":"arxiv-2408.11911","DOIUrl":null,"url":null,"abstract":"We define the Cartesian, Categorical, and Lexicographic, and Strong products\nof quantum graphs. We provide bounds on the quantum chromatic number of these\nproducts in terms of the quantum chromatic number of the factors. To adequately\ndescribe bounds on the lexicographic product of quantum graphs, we provide a\nnotion of a quantum $b$-fold chromatic number for quantum graphs.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.11911","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
We define the Cartesian, Categorical, and Lexicographic, and Strong products
of quantum graphs. We provide bounds on the quantum chromatic number of these
products in terms of the quantum chromatic number of the factors. To adequately
describe bounds on the lexicographic product of quantum graphs, we provide a
notion of a quantum $b$-fold chromatic number for quantum graphs.
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