From Fan History Wiki
IntroductionTakaishi Takeru (TK) and Yagami Hikari (Kari Kamiya), two characters from Digimon. During the run of the second season of Digimon, in which Takeru and Hikari were main characters, this pairing was very popular, as popular as Taiora. It should be noted that Takari has 19 C2 communities dedicated to it on Fanfiction.net, compared with 15 for Taiora and 7 for Taito. The final episode of the season, which showed the characters from the first season as well as second season as adults, suggested the Takeru and Hikari were at least at one time together.
These two have a strong relationship, and it can be seen at the very beginning of season Adventure 02, and near the end of season 01 (with Piedmon). It's obvious that these two are close friends. Takeru and Hikari have more experiecne in the digital world in season 2, and that gives them an advantage. It is also noticed that their digimon are similar in digivolutions.
This section needs more information.
Some Takari fans bashed Motomiya Daisuke because he competed with Takeru for Hikari's affection. In season 2 (english), Daisuke(or Davis) has a major crush on Hikari(Kari). Kari, though, doesn't return these feelings. Please see the Motomiya Daisuke article for more details.