Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.     

Nitrosation of Phenolic Substrates under Mildly Basic Conditions: Selective Preparation of p-Quinone Monooximes and Their Antiviral Activities

Nitrosation of 3-methoxyphenol and 1-naphthol were examined under both acidic (NaNO(2)-EtCO(2)H-H(2)O) and basic (i-AmNO(2)-K(2)CO(3)-DMF) conditions. Acidic nitrosations afforded ortho-directed products, whereas para-directed nitrosations were observed under basic conditions to yield p-quinone monooximes. The basic para-directed nitrosation was further examined using 15 phenols, two naphthols, and four phenolic heterocyclics. A one-pot operation of the basic nitrosation followed by methylation with dimethyl sulfate gave the corresponding methyl ethers in high yield. Two p-quinone monooximes derived from 3-methoxyphenol and 8-hydroxyquinoline showed a moderate activity against HSV-1, and the latter oxime was also effective against HSV-2. On the other hand, p-quinone monooximes derived from methyl salicylate, 1-naphthol, 7-hydroxy-2-methylbenzo[b]furan, and 8-hydroxycoumarin showed the comparable activity to that of DDI against HIV-1.