Norms and perfect graphs

The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987.     

Catalyse heterogene en presence de sels et sans solvant : II. Hydrosilylation d'aldehydes et de cetones satures et α,β ethyleniques

Hydrosilylation of saturated and α,β-unsaturated carbonyl compounds by heterogeneous catalysis without solvent and in the presence of salts (HCO2K, o-Ph(CO₂K)₂, FK, FCs) was carried out with good yields. FCs is a very efficient salt for hydrosilylation of aldehydes and ketones: for instance α-NpSiH₃ reacts quantitatively at room temperature with PhCOPh giving α-NpSi(OCHPh₂)₃. With α,β-unsaturated ketones FCs leads to 1,2-addition. It allows the isomerization of allysilyl ethers in silyl enol ethers, providing that the transferring hydrogen is benzylic.