  Finding a marked vertex in a graph can be a complicated task when using
quantum walks. Recent results show that for two or more adjacent marked
vertices search by quantum walk with Grover's coin may have no speed-up over
classical exhaustive search. In this paper, we analyze the probability of
finding a marked vertex for a set of connected components of marked vertices.
We prove two upper bounds on the probability of finding a marked vertex and
sketch further research directions.
