Katy Perry had a Memorial Day bash at her new Hollywood Hills home on Monday, and Us Weekly reports that not only was John Mayer on the guest list, but that the two "seem to be back together -- or back together-ish." The guest added, "They were very flirty and having a really good time together. They have good chemistry."

The lovebirds first started dating in the summer of 2012, they broke up that August and then they got back together again in September, only to split again in March. "It's not over until it's over," a source told the mag after the couple's second break up. "You have to see how things play out."

Maybe the third time will be the charm for these two sexy singers? And at least K. Stew doesn't have to worry about these two shacking up ... but we're guessing Katy won't change her mind about the adulterous Twilight starlet...