diff --git a/BGL/include/CGAL/boost/graph/helpers.h b/BGL/include/CGAL/boost/graph/helpers.h
index df01fc634ac..630e7a974c8 100644
--- a/BGL/include/CGAL/boost/graph/helpers.h
+++ b/BGL/include/CGAL/boost/graph/helpers.h
@@ -777,29 +777,6 @@ void clear(FaceGraph& g)
   CGAL_postcondition(num_faces(g) == 0);
 }
 
-/**
- * \ingroup PkgBGLHelperFct
- *
- * returns the degree of the face with halfedge `hd`
- *
- * @tparam FaceGraph model of `FaceGraph`
- *
- * @param hd a halfedge of the face of interest
- * @param g the graph containing `hd`
- *
- **/
-template <typename FaceGraph>
-typename boost::graph_traits<FaceGraph>::degree_size_type
-face_degree(typename boost::graph_traits<FaceGraph>::halfedge_descriptor hd, const FaceGraph& g)
-{
-  typename boost::graph_traits<FaceGraph>::degree_size_type res = 0;
-  typename boost::graph_traits<FaceGraph>::halfedge_descriptor done = hd;
-  do {
-    ++res;
-    hd = next(hd,g);
-  }while(! (hd == done));
-  return res;
-}
 
 } // namespace CGAL
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/Scene_facegraph_item_k_ring_selection.h b/Polyhedron/demo/Polyhedron/Plugins/PMP/Scene_facegraph_item_k_ring_selection.h
index 8161a167afe..86168d363e0 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/Scene_facegraph_item_k_ring_selection.h
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/Scene_facegraph_item_k_ring_selection.h
@@ -154,7 +154,8 @@ public Q_SLOTS:
     if(active_handle_type == Active_handle::VERTEX || active_handle_type == Active_handle::PATH)
     {
 #ifdef USE_SURFACE_MESH
-      std::size_t h = reinterpret_cast<std::size_t>(void_ptr);
+      typedef boost::graph_traits<FaceGraph>::vertices_size_type size_type;
+      size_type h = reinterpret_cast<size_type>(void_ptr);
       process_selection( static_cast<fg_vertex_descriptor>(h) );
 #else
       process_selection( static_cast<Polyhedron::Vertex*>(void_ptr)->halfedge()->vertex() );
@@ -169,7 +170,8 @@ public Q_SLOTS:
       || active_handle_type == Active_handle::CONNECTED_COMPONENT)
     {
 #ifdef USE_SURFACE_MESH
-      std::size_t h = reinterpret_cast<std::size_t>(void_ptr);
+      typedef boost::graph_traits<FaceGraph>::faces_size_type size_type;
+      size_type h = reinterpret_cast<size_type>(void_ptr);
       process_selection( static_cast<fg_face_descriptor>(h) );
 #else
       process_selection( static_cast<Polyhedron::Facet*>(void_ptr)->halfedge()->facet() );
@@ -183,7 +185,8 @@ public Q_SLOTS:
     if(active_handle_type == Active_handle::EDGE)
     {
 #ifdef USE_SURFACE_MESH
-      std::size_t h = reinterpret_cast<std::size_t>(void_ptr);
+      typedef boost::graph_traits<FaceGraph>::edges_size_type size_type;
+      size_type h = reinterpret_cast<size_type>(void_ptr);
       process_selection( static_cast<fg_edge_descriptor>(h) );
 #else
       process_selection( edge(static_cast<Polyhedron::Halfedge*>(void_ptr)->opposite()->opposite(), *poly_item->polyhedron()) );
diff --git a/Polyhedron/demo/Polyhedron/Scene_polyhedron_item_k_ring_selection.h b/Polyhedron/demo/Polyhedron/Scene_polyhedron_item_k_ring_selection.h
index 82d238fc6f7..d3f729ede83 100644
--- a/Polyhedron/demo/Polyhedron/Scene_polyhedron_item_k_ring_selection.h
+++ b/Polyhedron/demo/Polyhedron/Scene_polyhedron_item_k_ring_selection.h
@@ -191,7 +191,8 @@ public Q_SLOTS:
   // slots are called by signals of surface_mesh_item
   void sm_vertex_has_been_selected(void* v)
   {
-    std::size_t h = reinterpret_cast<std::size_t>(v);
+    typedef boost::graph_traits<SMesh>::vertices_size_type size_type;
+    size_type h = reinterpret_cast<size_type>(v);
     is_active=true;
     if(active_handle_type == Active_handle::VERTEX || active_handle_type == Active_handle::PATH)
       process_selection( sm_vertex_descriptor(h) );
@@ -199,7 +200,8 @@ public Q_SLOTS:
   }
   void sm_facet_has_been_selected(void* v)
   {
-    std::size_t h = reinterpret_cast<std::size_t>(v);
+    typedef boost::graph_traits<SMesh>::vertices_size_type size_type;
+    size_type h = reinterpret_cast<size_type>(v);
     is_active=true;
     if (active_handle_type == Active_handle::FACET
       || active_handle_type == Active_handle::CONNECTED_COMPONENT)
@@ -208,7 +210,8 @@ public Q_SLOTS:
   }
   void sm_edge_has_been_selected(void* v)
   {
-    std::size_t h = reinterpret_cast<std::size_t>(v);
+    typedef boost::graph_traits<SMesh>::edges_size_type size_type;
+    size_type h = reinterpret_cast<size_type>(v);
     is_active=true;
     if(active_handle_type == Active_handle::EDGE)
       process_selection(sm_edge_descriptor(h) );
diff --git a/Polyhedron/demo/Polyhedron/Scene_polyhedron_selection_item.cpp b/Polyhedron/demo/Polyhedron/Scene_polyhedron_selection_item.cpp
index 5d44a3ca477..5831550c040 100644
--- a/Polyhedron/demo/Polyhedron/Scene_polyhedron_selection_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_polyhedron_selection_item.cpp
@@ -10,6 +10,7 @@
 
 #include <boost/unordered_map.hpp>
 #include <boost/unordered_set.hpp>
+#include <boost/range.hpp>
 
 #include <exception>
 #include <functional>
@@ -1176,9 +1177,9 @@ bool Scene_polyhedron_selection_item:: treat_selection(const std::set<fg_edge_de
     }
       //Join vertex
     case 0:
-      if(CGAL::face_degree(halfedge(ed, *polyhedron()), *polyhedron()) < 4
+      if(boost::distance(CGAL::halfedges_around_face(halfedge(ed, *polyhedron()), *polyhedron())) < 4
            ||
-         CGAL::face_degree(opposite(halfedge(ed, *polyhedron()),*polyhedron()),*polyhedron())< 4)
+         boost::distance(CGAL::halfedges_around_face(opposite(halfedge(ed, *polyhedron()),*polyhedron()),*polyhedron()))< 4)
         {
           d->tempInstructions("Edge not selected: the incident facets must have a degree of at least 4.",
                            "Select the edge with extremities you want to join.");
@@ -1258,7 +1259,9 @@ bool Scene_polyhedron_selection_item:: treat_selection(const std::set<fg_edge_de
     case 6:
 
         //check preconditions
-      if(CGAL::face_degree(halfedge(ed, *polyhedron()),*polyhedron()) == 3 && CGAL::face_degree(opposite(halfedge(ed, *polyhedron()),*polyhedron()),*polyhedron()) == 3)
+      if(boost::distance(CGAL::halfedges_around_face(halfedge(ed, *polyhedron()),*polyhedron())) == 3 
+         && 
+         boost::distance(CGAL::halfedges_around_face(opposite(halfedge(ed, *polyhedron()),*polyhedron()),*polyhedron())) == 3)
         {
           CGAL::Euler::flip_edge(halfedge(ed, *polyhedron()), *polyhedron());
           polyhedron_item()->invalidateOpenGLBuffers();