Judge James Meredith -- who handled the case in Smith County, Texas on Sunday following Mahomes Sr.'s DWI arrest -- tells us he didn't impose any travel ban on the elder Mahomes as part of his bond conditions ... paving the way for Dad to watch his son play in Las Vegas in SB LVIII.

Of course, it's unclear if the Chiefs star will want him there now following the added distraction in the leadup to the Big Game ... but, at least in the eyes of the law, Mahomes Sr. will be allowed to leave the state for it.

As part of the conditions of his bond, however, we're told Mahomes Sr. will not be able to take part in much partying in Sin City if he does make the trip. Law enforcement officials say he's been barred from possessing or consuming alcohol and/or illegal drugs. He's also been required to have an interlock device on his car -- as well as submit to random testing.

As we reported, Mahomes Sr. was thrown behind bars late Saturday night on a felony charge of driving while intoxicated.

A spokesperson for the Tyler Police Dept. said on Monday morning cops initially pulled over Mahomes Sr. at around 8:30 PM for a routine traffic stop ... though "evidence obtained during the stop led to the arrest."