I have installed opensuse on a TP 600X and it mostly works.
KDE seems to work correctly. When I try to use gnome, I get
a set of icons. Clicking the SuSE (lizardface), which I think
should show me a menu, I get a "Error Launching Application"
window, stating "There was an error launching the application."
Details: Failed to execute child process
"SuSEgreeter" (No such file or directory)

I have searched, and there is no such file.

History: I installed 9.0 from purchased CDs, then upgraded to
the remastered 10.1 by net install, then updated everything.

When you did the install of the 10.1 did you install KDE or Gnome?

As far as I know, I was doing both. That is, I didn't leave anything out
that I remember.

Is there a way to find out which particular package SuSEgreeter comes from?
I could then reinstall that package.

Go in to yast > software management, Then click selections from the filter drop down menu and see if "Gnome System" is installed.

In the box on the left, GNOME System is checked.

In the package list on the right, all the packages are checked,
but some of the package names are in red.

For the packages in red, the inst. version is newer than the
avail version.

The only installation source showing is
http://64.60.236/pub/opensuse/distri....1/inst-source (this is typed in by hand)

Ok that explanes it.
I have never been able to run both KDE and Gnome desktops on the same installation.
Your going to have to pick one to use.
I dumped Gnome a long time ago and use nothing but KDE on all of my boxes.
I found Gnome to be problematic.
I also dumped 10.1 and went back to 10.0 till 10.2 comes out on December 7th..