While the top-ranked Trojans wait weeks, months, or years to find out what comes out of the latest allegations, they’ll try to concentrate on improving a team that looked ready to contend with the nation’s best once again.

USC beat Hawaii, 49-10, in its season opener Saturday, but also learned that an employee of the Los Angeles County assessor’s office apparently gave gifts to long-departed tailback Joe McKnight and former basketball player Davon Jefferson.

Just when athletic director Pat Haden, USC president Max Nikias, and coaches Lane Kiffin and Kevin O’Neill might have thought they had fully cleaned up the mess left behind by former athletic director Mike Garrett and coaches Pete Carroll and Tim Floyd, more trouble surfaced in the report by the Los Angeles Times.

‘‘We have discussed those allegations with the NCAA and Pac-12, and we will thoroughly investigate them and take any and all necessary actions,’’ Haden said.

The Times report implicated Scott Schenter, the former appraiser who was already a peripheral figure in the Trojans’ troubles after he apparently loaned a Land Rover to Mc­Knight during the 2009 season.

The new report includes descriptions of illegal gifts including a different car, an airline ticket, and cash given to the two athletes by Schenter. The alleged infractions are still within the four-year statute of limitations set by the NCAA for pursuing punishment.

Until USC has a better idea of what the allegations will mean for its current Trojans, the school is likely to focus on a team that looked worthy of its preseason No. 1 ranking.

Kiffin wasn’t totally pleased with his star-studded offense despite headline-grabbing performances by Matt Barkley and Marqise Lee. He had few complaints about his dominant defense, though.

‘‘They’re the story of the day,’’ Kiffin said. ‘‘A lot of question marks there, and it seemed they made a bunch of plays tonight.’’

MVC makes noise

If the Big 12 ever wants to expand to 12 members again, the league’s powerbrokers might want to take a look at poaching a couple schools from the Missouri Valley Conference.

Of course, Kansas and Kansas State might quickly object. Both of them had to work hard against schools from the Football Championship Subdivision before winning their season openers Saturday. They weren’t alone, either: Wisconsin had to make a late defensive stand to beat Northern Iowa, Indiana State took Indiana to the brink, and Pittsburgh was embarrassed by Youngstown State in Paul Chryst’s debut as Panthers coach.

‘‘They might not be big-name schools, but you can’t sleep on them,’’ Kansas State defensive back Nigel Malone said shortly after the No. 22 Wildcats had to rattle off 35 fourth-quarter points to beat Missouri State, 51-9.

Also, South Dakota State gave Kansas everything it could handle before falling, 34-17, in Charlie Weis’s debut with the Jayhawks; Pittsburgh got dominated by Youngstown State, 34-17, in its first game under Chryst; and Northern Iowa nearly pulled off the biggest upset of all before a late rally fell short at Camp Randall Stadium in a 26-21 loss to the No. 12 Badgers.

Sooners get by

While the rest of the Big 12’s title contenders rolled to impressive victories, No. 4 Oklahoma clearly has a few things to tighten up after scraping past a supposedly overmatched opponent. The Sooners managed to pull out a 24-7 win over scrappy Texas-El Paso at the Sun Bowl Saturday night, but needed a strong effort from their defense and a pair of fourth-quarter touchdowns to do it. It wasn’t exactly what they had in mind, particularly after Oklahoma State scored 84 points and West Virginia dropped 69 in their easily-won openers. ‘‘It wasn’t pretty, we know that, but it’s a ‘W,’ ’’ Oklahoma co-offensive coordinator Josh Heupel said. ‘‘A lot of things we can go back and work on. It’s not big-picture things. There are a lot of fine-detail things we have to continue to iron out.’’ . . . Rich Rodriguez’s debut as coach at Arizona was a successful one — barely — as the Wildcats escaped with a 24-17 win over Toledo in overtime.

Louisville rolls

Jeremy Wright rushed for 105 yards and three touchdowns and Teddy Bridgewater passed for 232 yards, helping No. 25 Louisville start the season strong with a 32-14 victory against rival Kentucky Sunday in Louisville, Ky. . . . Nick Florence threw for 341 yards and four touchdowns in his first game since taking over for Heisman Trophy winner Robert Griffin III, leading Baylor to a 59-24 blowout of SMU Sunday night in Waco, Texas. Florence, who led the Bears to touchdowns on their first two drives, finished 21 of 30 and didn’t play in the fourth quarter.