To find the mapping from a desktop file entry to a program/package, is kind of magic from the yum POV. In theory you might expect to be able to do:
yum search solitaire
...and it will show either gnome-games or aisleriot as a package, however at least the gnome-games package doesn't show up here.
You can use google, "gnome solitare" will give you the aisleriot and gnome-games pages as the first two hits ... and the former does explicitly mention it is known as "sol" as well.
If you know that desktop files are in /usr/share/applications you can do:
% fgrep -i solitaire /usr/share/applications/*
...and that will tell you the filename which you can use "yum provides" on (or on the command name without that file).
Or you can do it the graphical way:
open the menu editor (alacarte -- can be found by "yum search menu editor")
Find menu entry you want to delete.
Look in properties for command name.
yum provides sol