diff --git a/BGL/include/CGAL/boost/graph/graph_traits_OpenMesh.h b/BGL/include/CGAL/boost/graph/graph_traits_OpenMesh.h
index a3eeb6c33d2..87f27b3f5ca 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_OpenMesh.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_OpenMesh.h
@@ -16,7 +16,6 @@
 #include <boost/graph/properties.hpp>
 
 #include <CGAL/boost/iterator/transform_iterator.hpp>
-#include <boost/graph/adjacency_iterator.hpp>
 
 #include <CGAL/boost/graph/internal/OM_iterator_from_circulator.h>
 #include <CGAL/boost/graph/iterator.h>
@@ -126,7 +125,7 @@ public:
 
   typedef CGAL::Out_edge_iterator<SM> out_edge_iterator;
 
-  typedef typename boost::adjacency_iterator_generator<SM, vertex_descriptor, out_edge_iterator>::type adjacency_iterator;
+  typedef CGAL::Vertex_around_target_iterator<SM> adjacency_iterator;
 
   // nulls
   static vertex_descriptor   null_vertex() { return vertex_descriptor(); }
@@ -270,12 +269,10 @@ out_edges(typename boost::graph_traits<OPEN_MESH_CLASS >::vertex_descriptor v,
 
 template <typename K>
 CGAL::Iterator_range<typename boost::graph_traits<OPEN_MESH_CLASS >::adjacency_iterator>
-adjacnt_vertices(typename boost::graph_traits<OPEN_MESH_CLASS >::vertex_descriptor v,
+adjaecnt_vertices(typename boost::graph_traits<OPEN_MESH_CLASS >::vertex_descriptor v,
                  const OPEN_MESH_CLASS& sm)
 {
-  typedef typename boost::graph_traits<OPEN_MESH_CLASS >::out_edge_iterator OutEdgeIter;
-  typedef typename boost::graph_traits<OPEN_MESH_CLASS >::adjacency_iterator Iter;
-  return CGAL::make_range(Iter(OutEdgeIter(halfedge(v,sm),sm), &sm), Iter(OutEdgeIter(halfedge(v,sm),sm,1), &sm));
+  return CGAL::vertices_around_target(v,sm);
 }
 
 
diff --git a/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h b/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h
index 7522828fa72..9914445e81a 100644
--- a/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h
+++ b/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS.h
@@ -20,7 +20,6 @@
 #include <boost/config.hpp>
 #include <boost/iterator/iterator_adaptor.hpp>
 #include <CGAL/boost/iterator/transform_iterator.hpp>
-#include <boost/graph/adjacency_iterator.hpp>
 #include <boost/type_traits/remove_const.hpp>
 
 #include <boost/graph/graph_traits.hpp>
@@ -181,7 +180,7 @@ public:
 
   typedef In_edge_iterator<HDS> in_edge_iterator;
 
-  typedef typename boost::adjacency_iterator_generator<HDS, vertex_descriptor, out_edge_iterator>::type adjacency_iterator;
+  typedef Vertex_around_target_iterator<HDS> adjacency_iterator;
 
   typedef boost::undirected_tag             directed_category;
   typedef boost::disallow_parallel_edge_tag edge_parallel_category;
diff --git a/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS_default.h b/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS_default.h
index 1a8484299fc..fa2f9141600 100644
--- a/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS_default.h
+++ b/HalfedgeDS/include/CGAL/boost/graph/graph_traits_HalfedgeDS_default.h
@@ -177,9 +177,7 @@ inline Iterator_range<typename boost::graph_traits< HalfedgeDS_default<T,I,A> co
 adjacent_vertices( typename boost::graph_traits< HalfedgeDS_default<T,I,A> const>::vertex_descriptor u
                    , const HalfedgeDS_default<T,I,A>& p)
 {
-  typedef typename boost::graph_traits< HalfedgeDS_default<T,I,A> const>::out_edge_iterator OutEdgeIter;
-  typedef typename boost::graph_traits< HalfedgeDS_default<T,I,A> const>::adjacency_iterator Iter;
-  return make_range(Iter(OutEdgeIter(halfedge(u,p),p),&p), Iter(OutEdgeIter(halfedge(u,p),p,1), &p));
+  return CGAL::vertices_around_target(u,p);
 }
 
 //
diff --git a/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex_for_combinatorial_map.h b/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex_for_combinatorial_map.h
index 36406f42275..0844df433fe 100644
--- a/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex_for_combinatorial_map.h
+++ b/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex_for_combinatorial_map.h
@@ -208,7 +208,7 @@ public :
   typedef CGAL::In_edge_iterator<CMap>  in_edge_iterator;
   typedef CGAL::Out_edge_iterator<CMap> out_edge_iterator;
 
-  typedef typename boost::adjacency_iterator_generator<CMap, vertex_descriptor, out_edge_iterator>::type adjacency_iterator;
+  typedef CGAL::Vertex_around_target_iterator<CMap> adjacency_iterator;
 
   // nulls
   static vertex_descriptor   null_vertex()   { return nullptr; }
@@ -400,9 +400,7 @@ CGAL::Iterator_range<typename boost::graph_traits<CGAL_LCC_TYPE>::adjacency_iter
 adjacent_vertices(typename boost::graph_traits<CGAL_LCC_TYPE>::vertex_descriptor v,
                   const CGAL_LCC_TYPE& lcc)
 {
-  typedef typename boost::graph_traits<CGAL_LCC_TYPE>::out_edge_iterator OutEdgeIter;
-  typedef typename boost::graph_traits<CGAL_LCC_TYPE>::adjacency_iterator Iter;
-  return make_range(Iter(OutEdgeIter(halfedge(v, lcc), lcc), &lcc), Iter(OutEdgeIter(halfedge(v, lcc), lcc, 1), &lcc));
+  return CGAL::vertices_around_target(v,lcc);
 }
 
 //
diff --git a/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h b/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h
index 78f66289eef..547b8374776 100644
--- a/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h
+++ b/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h
@@ -30,7 +30,6 @@
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/assertions.h>
 
-#include <boost/graph/adjacency_iterator.hpp>
 
 namespace boost {
 
@@ -85,7 +84,7 @@ public:
 
   typedef CGAL::Out_edge_iterator<SM> out_edge_iterator;
 
-  typedef typename boost::adjacency_iterator_generator<SM, vertex_descriptor, out_edge_iterator>::type adjacency_iterator;
+  typedef CGAL::Vertex_around_target_iterator<SM> adjacency_iterator;
 
   // nulls
   static vertex_descriptor   null_vertex() { return vertex_descriptor(); }
@@ -228,10 +227,7 @@ Iterator_range<typename boost::graph_traits<CGAL::Surface_mesh<P> >::adjacency_i
 adjacent_vertices(typename boost::graph_traits<CGAL::Surface_mesh<P> >::vertex_descriptor v,
                   const CGAL::Surface_mesh<P>& sm)
 {
-  typedef typename boost::graph_traits<CGAL::Surface_mesh<P> >::out_edge_iterator OutEdgeIter;
-  typedef typename boost::graph_traits<CGAL::Surface_mesh<P> >::adjacency_iterator Iter;
-  return make_range(Iter(OutEdgeIter(halfedge(v,sm),sm), &sm),
-                    Iter(OutEdgeIter(halfedge(v,sm),sm,1), &sm));
+  return CGAL::vertices_around_target(v,sm);
 }
 
 template<typename P>