Does Kernighan-Lin algorithm guarantee its partitions to be a connected graph?
The Kernighan-Lin algorithm tries to find a partition.  As far as I can tell, the partition it finds might or might not be connected; I don't see any guarantee that it will output a connected partition.  There is also no guarantee that it finds the optimal partition.  Even if the optimal partition is connected, I don't think there is any guarantee that the Kernighan-Lin algorithm will output a connected partition.