They were constantly attacking down the west side of Kiev, at one point last week cutting the direct highway Lviv-Kiev. But that seems to have stopped and the Ukes have the highway back.
No, they do not have the highway back. There are several groups of Russian troops sitting on the highway from Zhitomyr and from Korosten have Russian troops sitting on them and the bridges have been blown. There might be places where the Ukrainians control the highway, but they have to control it ALL to get supplies in.
The Russian only have to sit in one place and control the air. They don’t have to move at all and watch the Ukrainians starve in the cities.