While watching the television broadcast of last night's Texas at Texas A&M men's basketball game, I noticed a logo on the floor that is only used for Longhorn-Aggie athletic contests. UT and A&M have given an official name to their rivalry, the Lone Star Showdown. Any time the two schools meet in any sport, the winner earns points that are added up across sports at the end of the academic year. In addition, a Lone Star Showdown logo is shown on the playing field/court for some (if not all) other sports, including football (the adjoining photo, from a previous year's Longhorn-Aggie hoops battle, is from the Wikipedia page on the Showdown, cropped to highlight the logo by the referee).
Even though I'm based in Big 12 country (I'm a faculty member at Texas Tech) and watch a lot of men's and women's conference basketball, I had not noticed the logo until last night.
Other schools have similar rivalries. For example, UCLA and USC have a competition known as the Lexus Gauntlet (South), whereas Stanford and Cal have a northern California version of the Gauntlet, as well. I also watch a lot of Pac-Ten hoops (UCLA is my undergraduate alma mater), and I don't recall ever seeing a basketball floor decal for one of these rivalry games.