A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing protocol which detects if a set of processors is a cutset of an arbitrary rooted network. This protocol is based on the depth-first search ( ¢¡¤£ ) traversal and its properties. An interesting property of our protocol is that, despite the initial configuration, as soon as the protocol is initiated (by the root), the result obtained from the computations will be right. So, after the first execution, the root is able to take a decision: “the input set is a cutset or not”, and this decision is right.