No of course not!!!!!!!!its a fake rumour to gain the public's attention.They are still strong,and are still going out.On Twitter as well,it's been proved wrong.
Proof they didn't break up :) It says :
interviewer : About your beautiful girlfriend selena, how is she? and where is she?
Justin : She is in Bulgaria and she's filming a movie.
interviewer : aw we miss her
Justin : I know.