B757 FLT CREW IS FORCED TO APPLY HEAVY BRAKING TO AVOID ANOTHER ACFT WHILE TAXIING FOR TKOF.

Narrative

WE WERE STOPPED AT AN INTXN SHORT OF TXWY G. GND CLRED US TO TAXI TO RWY 18L VIA TXWY G. WE PROCEEDED N ON TXWY G. APCHING AN INTXN WE SAW A B737 COMING OFF THEIR RAMP AT A HIGH RATE OF SPD. I ASKED THE FO IF THAT GUY WAS GOING TO STOP; BUT BEFORE HE COULD ANSWER I REALIZED HE WAS NOT. I IMMEDIATELY APPLIED AGGRESSIVE BRAKING AND STEERED TO THE R TO AVOID A COLLISION. WE GOT STOPPED JUST AS THE ACFT WINGTIP PASSED ABOUT 25 FT IN FRONT OF OUR NOSE. IF I HAD NOT TAKEN THE EVASIVE ACTION I DID WE WOULD HAVE DEFINITELY COLLIDED. I QUERIED MY CREW TO MAKE SURE EVERYONE ONBOARD WAS ALRIGHT; THEN CONTINUED TO TAXI. I ASKED THE GND CTLR IF HE HAD SEEN WHAT JUST HAPPENED. HE TOLD ME TO STAND BY. I WAITED AND FINALLY GOT A NUMBER TO CALL. AFTER LNDG I CALLED THE TWR SUPVR AND WAS TOLD NEITHER ACFT HAD BEEN GIVEN HOLD SHORT OR YIELD INSTRUCTIONS. I FEEL SOMEONE SHOULD HAVE; BUT HAVING NONE THE ACFT; TO MY L; SHOULD HAVE YIELDED TO ME; ON HIS R AND ON AN ACTIVE TXWY. INSTEAD; HE TAXIED SO FAST TO BEAT US OUT THAT I SAW SMOKE COMING OFF HIS NOSEWHEEL TIRES AS HE MADE THE TURN IN FRONT OF US WHILE I WAS TAKING EVASIVE ACTION.