The phrase "college classmate" is correct and usable in written English.
For example: "My college classmate was always very helpful in our group projects."
He had married a college classmate, Norma Peterson, in 1950.
I learned that a college classmate was the great-granddaughter of Buffalo Bill's best friend.
In the morning, it still wouldn't come — an old college classmate of mine.
Brian Roach, a college classmate, said, "You just knew: don't bring it up".
And then — this won't come as any surprise to mystery aficionados — the college classmate is eliminated.
A college classmate said that he was an eager participant in impromptu skits and plays.
Nobody else did this: only Walker Field, my neighbor, my college classmate, my old reliable.
She tells about a college classmate, Noonie Gerstein from Houston, Tex.
The narrator met Arun while visiting his niece Gita Banerjee, her college classmate, in Delhi.
"Everything she does is snappy," says her college classmate Henrietta Moore.
