Circular Chromatic Number and Mycielski Graphs

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• 作者：Genghua Fan
• 关键词：Mathematics SubjectClassification (2000) ; 05C15
• 刊名：Combinatorica
• 出版年：2004
• 出版时间：January 2004
• 年：2004
• 卷：24
• 期：1
• 页码：127-135
• 全文大小：173 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1439-6912

文摘

As a natural generalization of graph coloring, Vinceintroduced the star chromatic number of a graphG and denoted it by$ \chi {\left( G \right)} \geqslant \frac{{n + 3}} {2} $ \chi {\left( G \right)} \geqslant \frac{{n + 3}} {2} , then_c(M(G))=(M(G)). Let S be the set of vertices of degreen–1 inG. It is proved that if|S| 3, then_c(M(G))=(M(G)), and if |S| 5, then _c(M2(G))=(M2(G)), which implies the known results ofChang, Huang, and Zhu that if n3, _c(M(K_n))=(M(K_n)), and ifn5, then_c(M2(K_n))=(M2(K_n)).