This correction is due to Omri Liba of Ben-Gurion University of the Negev, Israel.
<p>

The Explorer algorithm is incorrect. Here is a counterexample (see the
picture below). Assume the faulty node is located in a completely
connected subcomponent <i>V</i>, and node <i>a</i> in
component <i>D</i>.  Suppose node <i>a</i> starts the message
propagating the information about its neighborhood as described in
Explorer.  Meanwhile, the faulty node starts a message carrying the
correct neighborhood of node <i>a</i> and the whole set of
nodes <i>N = V + D</i> as a visited set.
<p>

Node <i>p</i> then sends a message that originates from <i>a</i> to
its neighboring node <i>c</i>. Concurrently, node <i>c</i> sends a
message that originates in the faulty node to <i>p</i>. Since the
faulty message contains the whole set of nodes as visited set, once
process <i>p</i> receives this message from <i>c</i>, <i>p</i>
discards the message. Similarly, <i>c</i> discards a message received
from <i>p</i>. In the same manner processes on the border of <i>V</i>
and <i>D</i> fail to make progress in message propagation and
neighborhood of <i>a</i> is never confirmed. Specifically, this
discussion shows that <i>Proposition 1</i> is incorrect.

<img src=topology.errata.png height=500>