The usual thing to do when you have a recursive routine that needs an IUO parameter, is to use a 'helper' wrapper that supplies it.

Here's a cleaned up and simplified version that does that:

#! perl -slw
#! perl -slw
use strict;
use List::Util qw[ shuffle ];
use Data::Dump qw[ pp ];

my %graph = map {
  ( chr( 64 + $_ ) => [ (shuffle 'A'...'Z')[ 0 .. 1+ int( rand 10 )] ]
+ )
} 1, (shuffle 2 .. 25)[ 0.. int( rand 20 )], 26;

pp \%graph;

sub _findPaths {
    my( $graph, $start, $end, $seen ) = @_;

    return [$end] if $start eq $end;

    $seen->{ $start } = 1;
    map {
        map [ $start, @$_ ], _findPaths( $graph, $_, $end, {%$seen} );
    }  grep !$seen->{ $_ }, @{ $graph->{ $start } };
}

sub findPaths { _findPaths( @_, {} ); }

my( $start, $end ) = @ARGV;

print "@$_" for findPaths( \%graph, $start, $end );

__END__
c:\test>868031 A Z
{
  A => ["M", "L", "V", "Y", "C", "T", "X", "B", "U", "G", "J"],
  B => ["U", "W", "E", "Q", "M", "G", "N"],
  H => ["K", "L", "I", "S", "B", "H", "M", "P", "Q", "N", "T"],
  L => ["Q", "X", "E", "D", "L", "S", "N", "K"],
  P => ["D", "O", "Y", "R", "I", "W", "Q", "V", "N"],
  Q => ["P", "A", "N", "X", "R", "M", "T", "H", "O", "V"],
  R => ["O", "A", "S", "V", "M"],
  T => ["J", "Z", "F", "T", "Q", "X", "S"],
  V => ["L", "E", "Z", "V"],
  Y => ["M", "X", "Y", "I", "K", "U", "G", "S"],
  Z => ["M", "F", "A", "P", "I"],
}

A L Q P R V Z
A L Q P V Z
A L Q R V Z
A L Q T Z
A L Q H P R V Z
A L Q H P V Z
A L Q H T Z
A L Q V Z
A V L Q T Z
A V L Q H T Z
A V Z
A T Z
A T Q P R V Z
A T Q P V Z
A T Q R V Z
A T Q H P R V Z
A T Q H P V Z
A T Q V Z
A B Q P R V Z
A B Q P V Z
A B Q R V Z
A B Q T Z
A B Q H P R V Z
A B Q H P V Z
A B Q H T Z
A B Q V Z
[download]

Be warned. The random tree generator can generate some pretty big results sets.