Minimum edge ranking spanning trees of split graphs

Given a graph G, the minimum edge ranking spanning tree problem (MERST) is to find a spanning tree of G whose edge ranking is minimum. However, this problem is known to be NP-hard for general graphs. In this paper, we show that the problem MERST has a polynomial time algorithm for split graphs, which have useful applications in practice. The result is also significant in the sense that this is a first non-trivial graph class for which the problem MERST is found to be polynomially solvable. We also show that the problem MERST for threshold graphs can be solved in linear time, where threshold graphs are known to be split.     

A symmetric oxyselenenylation of simple olefins using optically active selenobinaphthyls

Asymmetric trans-addition reactions of simple olefins have been performed by using optically active 2-selenobinaphthyls 1 , 2a–g. Introduction of an amide group at the 2′-position in the binaphthyl skeleton enhances considerably the diastereomeric excess (de) of the asymmetric methoxyselenenylation. In the case of trans-olefins, introduction of another chiral center in the amide group further enhances the de due to double stereodifferentiation between the (R)-binaphthyl skeleton and the chiral amide group introduced at the 2′-position in the binaphthyl skeleton. The use of chiral nucleophiles is also effective to enhance the de for symmetrical cis-olefins.