Zhao, Yan The Hopf algebra structures of perfect graphs and perfect 2-partite graphs. (Chinese. English summary) Zbl 1150.05351 J. Qufu Norm. Univ., Nat. Sci. 33, No. 3, 25-29 (2007). Summary: In this paper, three Hopf algebras on the vector spaces of perfect graphs, perfect 2-partite graphs and perfect \(r\)-partite graphs, respectively, are constructed. The isomophisms between the three Hopf algebras and the polynomial Hopf algebras in one, two and \(r\)-indeterminates, respectively, are obtained. MSC: 05C17 Perfect graphs 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 16W30 Hopf algebras (associative rings and algebras) (MSC2000) Keywords:Hopf algebra; perfect graph; perfect 2-partite graph; perfect \(r\)-partite graph; polynomial Hopf algebra PDFBibTeX XMLCite \textit{Y. Zhao}, J. Qufu Norm. Univ., Nat. Sci. 33, No. 3, 25--29 (2007; Zbl 1150.05351)