×

The Hopf algebra structures of perfect graphs and perfect 2-partite graphs. (Chinese. English summary) Zbl 1150.05351

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)
PDFBibTeX XMLCite