The Southwest Conference, which has dominated college sports in Texas since 1915, appears headed for extinction.

Texas, Texas A&M, Baylor -- original members of the S.W.C. -- and Texas Tech have received informal offers to join the Big Eight Conference. That would leave Rice, Houston, Texas Christian and Southern Methodist to fend for themselves.

"All I can say is, we have an informal invitation," the University of Texas president, Robert Berdahl, said. The decision will be made by the school's board of regents, he said.

The four Southwest Conference schools would join the Big Eight in a 12-team league that would be in a better position to bargain for television contracts when the current broadcast deal ends in 1996.