The fact that is claimed to be true in part b) of problem 23-2 
is not true the way it is stated.


The fact that you have to prove is the following:
(Here I state the if and the only if part separately)

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If part:
--------

If there is no back edge (u,w) s.t. in G_p   u  is a descendant 
                           of v and w is a proper ancestor of v
then v is an articulation point of G.


                            AND

Only-If part:
-------------

If v is an articulation point of G 
then  there is no back edge (u,w) s.t. in G_p  u is a descendant
of v and w is a proper ancestor of v (where u belongs to the 
subtree of v that becomes disconnected from the rest of the graph
G if we remove v).
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The reason that I changed the Only-If part is that there may be 
a back edge from some descendant of v and still v be an 
articulation point.


Regards, 
Vasileios Megalooikonomou