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Theme Duels in Yu-Gi-Oh! Ultimate Masters: World Championship Tournament 2006 are duels where you duel against special opponents that do not appear in free duels. Also, there are deck-bound and duel-bound conditions that a player must fulfill and win the duel to clear it (e.g. "F.G.D" where you should deliver massive Battle Damage or "Green Gadget" where you must Normal Summon 10 times) hence the Theme.
If a player happens to defy a Limited Duel's deck-bound condition, they'll be alerted of the lack of certain cards in their deck and the Duel won't start. While defying a Limited Duel's duel-bound condition results in incompletion even if they win the Duel.