It is called US-Mexico border. If you mean the name of the river that defines much of that border, it is called the Rio Grande river (or Rio Bravo del Norte in Mexico).
Much of the border between Mexico and Texas is the Rio Grande River. The Rio Grande begins in the San Juan Mountains in Colorado and empties into the Gulf of Mexico.
The border between Texas and Mexico is the Rio Grande River.
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The Red river forms Texas southwest. The Rio Grande forms the southwest border between Texas and Mexico.
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Yes, the Rio Grande River is in Texas and forms a part of the border between Texas and Mexico.
The Colorado River forms the boundary between Arizona and California.