Roy Williams likes for his Kansas University basketball team to play a difficult schedule.

A murderous schedule is a different matter entirely, and Williams, KU’s 15th-year coach, believes tonight’s KU-Wyoming contest pushes the Jayhawks’ 2002-03 slate into the “killer” category.

Tipoff for the matchup between the No. 12-ranked Jayhawks (11-3) and the unranked Cowboys (12-2) is 8:05 p.m. at Allen Fieldhouse. It’ll be shown live on ESPN2 (cable channel 49).

“I didn’t really want Wyoming. Our schedule is so tough we didn’t need Wyoming coming in here because they are 12-2 and a heck of a team. They are a better team than I wanted,” Williams said of the Cowboys, who are receiving votes in the Associated Press poll after beating Texas Tech and South Carolina.

In last season’s NCAA Tournament, Wyoming knocked off Gonzaga, 73-66, and lost a close game to Arizona, 68-60.

“I wanted one of those double-directionals — Southwest East Louisiana State Seminary School, or somebody like that,” Williams said. “It worked out we couldn’t get anybody else like that.”

So KU’s coach accepted a one-time TV date with the Mountain West Conference squad, led by fifth-year coach Steve McClain, who directed Hutchinson Community College to a national junior college title in 1994.

“It’s going to be a heck of a game in the fieldhouse,” Williams said.

“This was a date-driven game,” said KU senior associate athletic director Richard Konzem, aware that Oregon, Tulsa, UCLA, Cal-Berkeley, Arizona, North Carolina and Florida already constituted the 21st toughest schedule in the country in the RPI index.

“We lost a week (to schedule nonconference games) in late November because of the Preseason NIT, and we lost the first week of January because we were the first Big Monday game with everybody else opening Saturday. It was down to finding somebody to play on this particular Wednesday.”

Wyoming had an open date available, and the rest is history.

“Every year we’ve gone and played a rough game right before the start of league play,” McClain said.

Last season, UW lost 90-84 on Jan. 1 at Texas Tech. Four days later, the Cowboys defeated UNLV, 69-59, for its first win over the Runnin’ Rebels in 20 years. In 2000-01, the Cowboys wrapped up nonconference play with a 73-69 loss at LSU. Five days later, they lost the league opener, 83-71, at Utah, but won their next six Mountain West games en route to claiming a share of the league crown.

“It gives us a reality check, an opportunity to see what your team is about and see things you’ll have to deal with in a league like ours,” McClain said.

Wyoming has won nine straight games — five in a row since losing senior forward Marcus Bailey for the season. Bailey, a three-year starter who averaged 15.6 points and 4.3 rebounds a game, tore his right anterior cruciate ligament in the second half of the Cowboys’ 77-63 victory over South Carolina on Dec. 19 in Laramie, Wyo.

“I believe if you have a player go down, you can replace his points and rebounds,” McClain said of Bailey. “I don’t know yet we have somebody who will replace Marcus’ toughness and ability in big games to come up with big plays.”

Wyoming is led by Uche Nsonwu-Amadi, a 6-foot-10, 260-pound senior from Nigeria, who averages 14.2 points and 11.1 rebounds. Donta Richardson, a 6-2 senior, averages 15.9 points and 3.3 boards. The Cowboys’ other starters are Jay Straight, a 5-11 guard who averages 7.8 points a game; Joe Ries, a 6-8 junior who averages 7.4 points; and David Rottinghaus, a 6-5 junior who averages 4.9 points per game.

Wyoming averages 76.2 points a game off 44.9 percent shooting, while allowing 65.1 points. Opponents are hitting 40.7 percent from the floor.

The Jayhawks, who have won eight straight games, average 87.5 points off 48.1 percent shooting, while allowing 56.5 points off 37.2 percent marksmanship.

“Coming into Allen Fieldhouse, you are walking into a very hard environment,” McClain said. His squad’s only losses have been to College of Charleston (81-72) in the Great Alaska Shootout and at Washington (79-70).

“We are excited about it. Our players look at it as an opportunity to face one of the top teams in the country on their floor, let it all hang out and see what happens.”

Of course, he believes the two-time defending conference champion Cowboys have a chance despite the Jayhawks’ 22-game nonconference home winning streak.

“Our players have played in plenty of big games. They understand once you tip it up it’s about execution and doing things right,” McClain said. “If you do that, you have an opportunity at the end. Our kids understand that as much as anyone.”