diff --git a/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h b/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
index aad31663753..c6f21af88fa 100644
--- a/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
+++ b/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
@@ -135,18 +135,18 @@ public:
     Constructs a primitive.
   */
   template <class Iterator>
-  AABB_face_graph_triangle_primitive(Iterator it, FaceGraph& graph, VertexPointPMap vppm)
+  AABB_face_graph_triangle_primitive(Iterator it, const FaceGraph& graph, VertexPointPMap vppm)
     : Base( Id_(*it),
-            Triangle_property_map(&graph,vppm),
-            Point_property_map(&graph,vppm) )
+            Triangle_property_map(const_cast<FaceGraph*>(&graph),vppm),
+            Point_property_map(const_cast<FaceGraph*>(&graph),vppm) )
   {}
 
 #ifndef DOXYGEN_RUNNING
   template <class Iterator>
-  AABB_face_graph_triangle_primitive(Iterator it, FaceGraph& graph)
+  AABB_face_graph_triangle_primitive(Iterator it, const FaceGraph& graph)
     : Base( Id_(*it),
-            Triangle_property_map(&graph),
-            Point_property_map(&graph) )
+            Triangle_property_map(const_cast<FaceGraph*>(&graph)),
+            Point_property_map(const_cast<FaceGraph*>(&graph)) )
   {}
 #ifndef CGAL_NO_DEPRECATED_CODE
   // for backward compatibility with Polyhedron::facets_begin()
@@ -171,9 +171,9 @@ public:
   /// \internal
   static
   typename Cstr_shared_data::Shared_data
-  construct_shared_data(FaceGraph& graph)
+  construct_shared_data(const FaceGraph& graph)
   {
-    return Cstr_shared_data::construct_shared_data(graph);
+    return Cstr_shared_data::construct_shared_data(const_cast<FaceGraph&>(graph));
   }
 
 };
diff --git a/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h b/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
index 1036c088000..000463376bb 100644
--- a/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
+++ b/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
@@ -121,18 +121,18 @@ public:
   is available with `vppm` set to `boost::get(vertex_point, graph)`.
   */
   template <class Iterator>
-  AABB_halfedge_graph_segment_primitive(Iterator it, HalfedgeGraph& graph, VertexPointPMap vppm)
+  AABB_halfedge_graph_segment_primitive(Iterator it, const HalfedgeGraph& graph, VertexPointPMap vppm)
     : Base( Id_(*it),
-            Segment_property_map(&graph, vppm),
-            Point_property_map(&graph, vppm) )
+            Segment_property_map(const_cast<HalfedgeGraph*>(&graph), vppm),
+            Point_property_map(const_cast<HalfedgeGraph*>(&graph), vppm) )
   {}
 
   #ifndef DOXYGEN_RUNNING
   template <class Iterator>
-  AABB_halfedge_graph_segment_primitive(Iterator it, HalfedgeGraph& graph)
+  AABB_halfedge_graph_segment_primitive(Iterator it, const HalfedgeGraph& graph)
     : Base( Id_(*it),
-            Segment_property_map(&graph),
-            Point_property_map(&graph) ){}
+            Segment_property_map(const_cast<HalfedgeGraph*>(&graph)),
+            Point_property_map(const_cast<HalfedgeGraph*>(&graph)) ){}
   #endif
 
   /// \internal
@@ -140,9 +140,9 @@ public:
   /// \internal
   static
   typename Cstr_shared_data::Shared_data
-  construct_shared_data(HalfedgeGraph& graph)
+  construct_shared_data(const HalfedgeGraph& graph)
   {
-    return Cstr_shared_data::construct_shared_data(graph);
+    return Cstr_shared_data::construct_shared_data(const_cast<HalfedgeGraph&>(graph));
   }
 };
 
diff --git a/Intersections_3/test/Intersections_3/test_intersections_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_3.cpp
index 2e3af429b25..28004cd5e78 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_3.cpp
@@ -479,7 +479,7 @@ struct Test {
     std::cout << "Bbox - Triangle\n";
 
     typedef CGAL::Polyhedron_3<K> Polyhedron;
-    typedef CGAL::AABB_face_graph_triangle_primitive<const Polyhedron> Primitive;
+    typedef CGAL::AABB_face_graph_triangle_primitive<Polyhedron> Primitive;
     typedef CGAL::AABB_traits<K, Primitive> Traits;
     typedef CGAL::AABB_tree<Traits> Tree;