diff --git a/BGL/include/CGAL/boost/graph/split_graph_into_polylines.h b/BGL/include/CGAL/boost/graph/split_graph_into_polylines.h
index f6af9843234..204a1b02743 100644
--- a/BGL/include/CGAL/boost/graph/split_graph_into_polylines.h
+++ b/BGL/include/CGAL/boost/graph/split_graph_into_polylines.h
@@ -221,7 +221,9 @@ The polylines are reported using a visitor.
         - <code>void start_new_polyline()</code>
           called when starting the description of a polyline.
         - <code>void add_node(typename boost::graph_traits<Graph>::%vertex_descriptor v)</code>
-          called for each vertex `v` of the polyline currently described.
+          called for each vertex `v` of the polyline currently described. If the polyline is closed
+          this function will be called twice for the first vertex of the cycle picked (once after
+          calling `start_new_polyline()` and once before the call to `end_polyline()`.
         - <code>void end_polyline()</code>
           called when the description of a polyline is finished.
 \tparam IsTerminal A functor providing `bool operator()(boost::graph_traits<Graph>::%vertex_descriptor v, const Graph& g) const`
diff --git a/Surface_mesh_skeletonization/include/CGAL/Mean_curvature_flow_skeletonization.h b/Surface_mesh_skeletonization/include/CGAL/Mean_curvature_flow_skeletonization.h
index 489358e2350..b732ab9437b 100644
--- a/Surface_mesh_skeletonization/include/CGAL/Mean_curvature_flow_skeletonization.h
+++ b/Surface_mesh_skeletonization/include/CGAL/Mean_curvature_flow_skeletonization.h
@@ -810,14 +810,14 @@ public:
 
   /// When using the low level API it is possible to access the intermediate
   /// results of the skeletonization process, called meso-skeleton.
-  /// It is a triangulated surface mesh which is model of `FaceListGraph`.
+  /// It is a triangulated surface mesh which is model of `FaceListGraph` and `HalfedgeListGraph`.
 #ifdef DOXYGEN_RUNNING
   typedef unspecified_type Meso_skeleton;
 #else
   typedef mTriangleMesh Meso_skeleton;
 #endif
   /// Reference to the collapsed triangulated surface mesh.
-  Meso_skeleton& meso_skeleton()
+  const Meso_skeleton& meso_skeleton() const
   {
     return m_tmesh;
   }