  In this paper we consider the separate coding problem for $L+1$ correlated
Gaussian memoryless sources. We deal with the case where $L$ separately encoded
data of sources work as side information at the decoder for the reconstruction
of the remaining source. The determination problem of the rate distortion
region for this system is the so called many-help-one problem and has been
known as a highly challenging problem. The author determined the rate
distortion region in the case where the $L$ sources working as partial side
information are conditionally independent if the remaining source we wish to
reconstruct is given. This condition on the correlation is called the CI
condition. In this paper we extend the author's previous result to the case
where $L+1$ sources satisfy a kind of tree structure on their correlation. We
call this tree structure of information sources the TS condition, which
contains the CI condition as a special case. In this paper we derive an
explicit outer bound of the rate distortion region when information sources
satisfy the TS condition. We further derive an explicit sufficient condtion for
this outer bound to be tight. In particular, we determine the sum rate part of
the rate distortion region for the case where information sources satisfy the
TS condition. For some class of Gaussian sources with the TS condition we
derive an explicit recursive formula of this sum rate part.
