Pan,
When a board member from one company sits on another board, that is called an interlocking directorates...which are illegal if the companies are direct competitors.
When a board member from Texaco sits on Kellog's, board, and a member from Chevron sits on Kellog's board, that becomes an indirect interlocking directorates. They are not illegal, and there really isn't a way to make them so becuase we can't stop people from sitting on more than one board--just from obviously colluding as they would do if they all sat on chevron's board and texaco's board together.
I pulled this article up and thought you would be interested in the graphs within it. This ownership graph closely resembles the ties of ownership over assets in the US, in general. The picture portrayed is not limited to Big Oil...
--
http://www.mtholyoke.edu/acad/intrel/Petroleum/ftc2.htm