diff --git a/BGL/include/CGAL/boost/graph/Face_filtered_graph.h b/BGL/include/CGAL/boost/graph/Face_filtered_graph.h
index e18921b5ef9..e634bd18184 100644
--- a/BGL/include/CGAL/boost/graph/Face_filtered_graph.h
+++ b/BGL/include/CGAL/boost/graph/Face_filtered_graph.h
@@ -25,6 +25,7 @@
 #include <CGAL/boost/graph/properties.h>
 #include <CGAL/boost/graph/iterator.h>
 #include <CGAL/boost/graph/named_function_params.h>
+#include <CGAL/boost/graph/helpers.h>
 #include <CGAL/assertions.h>
 #include <boost/foreach.hpp>
 #include <boost/unordered_set.hpp>
@@ -898,7 +899,7 @@ next(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMa
     return next(h, w.graph());
 
   //h is on the border of the selection
-  CGAL_assertion( !w.is_in_cc(face(h, w.graph())) );
+  CGAL_assertion( is_border(h, w.graph()) || !w.is_in_cc(face(h, w.graph())) );
   typedef typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h_d;
   h_d candidate = next(h, w.graph());
   CGAL_assertion(!w.is_in_cc(candidate));
@@ -923,7 +924,7 @@ prev(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMa
     return prev(h, w.graph());
 
   //h is on the border of the selection
-  CGAL_assertion( !w.is_in_cc(face(h, w.graph())) );
+  CGAL_assertion( is_border(h, w.graph()) || !w.is_in_cc(face(h, w.graph())) );
   typedef typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h_d;
   h_d candidate = prev(h, w.graph());
   CGAL_assertion(!w.is_in_cc(candidate));