It is not sufficient for the king to be on a secure
file or rank, to force a draw against king and oddling
it has to be in the secure corner.
Here is how to mate the black king with king and
oddling:
White: Og7,Kh6 Black: Kf8
First, White brings its king to h8, than it pushes
its king forward using zugzwang until it reaches d8.
White forces the Black king to a8. Now the finale:
Kc7! Ka7
Og5 Ka6
Oe5 Ka7
Oa5++
J'org Knappen