newscaster,
The 3x weekly non stop 772 flights you see is an error and if you check the flight number you'll see its MS9731, so it seems Egyptair (who codeshare with KE on the route) have messed up their ICN schedule.
For the summer KE flights to CAI are:
KE951 ICN/CAI 21:30/09:10 M-W-F-- A333 via DXB
KE952 CAI/ICN 11:10/08:20 -T-T-S- A333 via DXB
In the winter (from 31/10/05) they will have 2x weekly non-stop flights with B772.
"I thought BA would only be allowed in on their own and not through differnt franchises."
Well GB Airways and British Mediterranean are independant airlines and they are not owned by BA. And remember Astraeus also have scheduled flights from London to Egypt. So in theory there are 4 UK airlines operating scheduled flights to Egypt