{"title":"同阶非同构群的群着色和群连通性","authors":"Rikke Langhede, Carsten Thomassen","doi":"10.1016/j.ejc.2023.103816","DOIUrl":null,"url":null,"abstract":"<div><p>For every natural number <span><math><mi>k</mi></math></span>, there exists a planar graph which is <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msubsup></math></span>-colorable, but not <span><math><mi>Γ</mi></math></span>-colorable for any other Abelian group <span><math><mi>Γ</mi></math></span> of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span>. Its dual graph is <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msubsup></math></span>-connected, but not <span><math><mi>Γ</mi></math></span>-connected for any other Abelian group <span><math><mi>Γ</mi></math></span> of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span>.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669823001336/pdfft?md5=4d2c19bd40b56019f9f9869e2dedb235&pid=1-s2.0-S0195669823001336-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Group coloring and group connectivity with non-isomorphic groups of the same order\",\"authors\":\"Rikke Langhede, Carsten Thomassen\",\"doi\":\"10.1016/j.ejc.2023.103816\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For every natural number <span><math><mi>k</mi></math></span>, there exists a planar graph which is <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msubsup></math></span>-colorable, but not <span><math><mi>Γ</mi></math></span>-colorable for any other Abelian group <span><math><mi>Γ</mi></math></span> of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span>. Its dual graph is <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msubsup></math></span>-connected, but not <span><math><mi>Γ</mi></math></span>-connected for any other Abelian group <span><math><mi>Γ</mi></math></span> of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span>.</p></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0195669823001336/pdfft?md5=4d2c19bd40b56019f9f9869e2dedb235&pid=1-s2.0-S0195669823001336-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0195669823001336\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669823001336","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Group coloring and group connectivity with non-isomorphic groups of the same order
For every natural number , there exists a planar graph which is -colorable, but not -colorable for any other Abelian group of order . Its dual graph is -connected, but not -connected for any other Abelian group of order .
期刊介绍：
The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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