Keima Go / No Ko

Keima Go has no cycle of length 2 on any MxN board.

This is because however one keima captures the other, some intersections (those marked) would have to switch from black to white or vice versa in the recapture (liberty filling stones omitted):

Case 1  

Case 2  

Case 3  

Case 4  

However, here's a keima ko on a cylinder:

Keima Ko  

The two marked stones obviously form a keima, but their liberties do as well if "ends" of each horizontal line join behind.

Black can capture both marked stones in one move. White may only recapture after a ko threat.

An ogeima ko, by the way, needs no special board:

Ogeima Ko