A war of egos has erupted between super – golfer Tiger Woods and his gold-medal girlfriend Lindsey Vonn!

The accomplished athletes have been at odds ever since alpine skier Lindsey, 29, an­nounced her intention to represent the U.S. in the Winter Olympics in Sochi, Russia, in February – because Tiger says he may be too busy playing in golf tournaments to cheer her on.

While Lindsey has publicly downplayed the drama, insid­ers say that the two have been battling behind the scenes over whether Tiger, 37, will be on the green adding to his trophy case or on the slopes supporting his lady love.

“Lindsey is demanding to be considered an equal, but she thinks Tiger still sees her only as a pretty accessory and doesn’t take her skiing career seriously,” a source told The ENQUIRER.

 Lindsey has been a fixture at Tiger’s side at tournaments while she recovered from a horrific tumbling crash on Feb. 5 – in which she fractured her tibia and tore ligaments in her right knee – on the slopes in Austria.

The Winter Olympics run from Feb. 7-23, with two of Lindsey’s possible events – the slalom and giant slalom – set for Feb. 18 and 21. But Tiger is sched­uled to play in the WGC-Accenture Match Play Champ during that time­frame, which would mean he WON’T be in Russia with Lindsey.

A source says Tiger is even considering playing at Pebble Beach (Feb. 3-9) and at the Northern Trust Open (Feb. 12- 16) – and his skiing sweetheart is fuming.

“The arguments have been very nasty,” said the source. “Lindsey told Tiger: ‘I sup­ported you this season. Now, it’s your turn to support me in public. I’m not just your cheer­leader – I’m a world class athlete too!’”

But Tiger doesn’t think Lind­sey has any right to make demands on his time, says the source.

“Tiger is self­ish and thinks he’s much more important that any woman he might be with,” explained the source. “Mean­while, Lindsey’s sick of just being an ornament on his arm at events.

“It’s a serious clash of athlete egos, and neither one is willing to back down.”