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A class of weakly perfect graphs

H. R. Maimani, M. R. Pournaki, S. Yassemi (2010)

Czechoslovak Mathematical Journal

A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given.

A note on some discrete valuation rings of arithmetical functions

Emil Daniel Schwab, Gheorghe Silberberg (2000)

Archivum Mathematicum

The paper studies the structure of the ring A of arithmetical functions, where the multiplication is defined as the Dirichlet convolution. It is proven that A itself is not a discrete valuation ring, but a certain extension of it is constructed,this extension being a discrete valuation ring. Finally, the metric structure of the ring A is examined.

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