Well, all of the titles contain colors, but I'm sort of afraid that's too obvious to be it...
All three stories have colors in their titles.
All three protagonists are male.
All three protagonists are experiencing a big turning-point in their lives: Harry facing a post-war, post-Voldemort period of his life, the Chinese prince facing the beginning of his boarding school days, and Graham facing a new life free of the trauma of his entrapment in the vanishing cabinet.
I seem to have a disadvantage in this challenge: when the new stories are posted, it is about 1:00 a.m. here in Oregon, so I must either stay up very late or get up very early to have a chance of being the first to spot the most obvious connection. Perhaps the best strategy is to search for obscure but "interesting" connections that will win bonus points (or else to set my alarm clock for 1:00 a.m.!)
I can't check this as can't link to all the stories (archive on a go slow) but
1)All three are featured stories?
2)All mention colours (wow, am I the first ) - but actually all the colours mentioned can be different shaded and aren't fixed.
Chartreuse can be yellow or green
Jade can be green or white
Blue - there are many many different shades on blue (so tenuous- ha ha)
3)They all sound like names given to an OC girlfriend of Sirius Black
Chatreuse de Montmerency
All three of the stories are either named after Coldplay songs or from the lyrics to a Coldplay song (Fix You and Yellow are both Coldplay songs, Cartoon Heart is a lyric from the Coldplay song Charlie Brown)