From Dallas Morning News.com:

Under the bill, Texans with a concealed handgun license would be able to carry handguns openly in a shoulder or belt holster. The Senate passed a similar bill last month.

Rep. Rafael Anchia, D-Dallas, said “unfettered open carry” is not allowed in any of the country’s 12 biggest cities. But if the bill becomes law, it would break new ground by permitting open carry of handguns in four of them — Houston, San Antonio, Dallas and Austin, he said.