diff --git a/BGL/include/CGAL/boost/graph/Euler_operations.h b/BGL/include/CGAL/boost/graph/Euler_operations.h
index f8c79165bc5..4ca35144f8a 100644
--- a/BGL/include/CGAL/boost/graph/Euler_operations.h
+++ b/BGL/include/CGAL/boost/graph/Euler_operations.h
@@ -12,10 +12,6 @@
 #ifndef CGAL_EULER_OPERATIONS_H
 #define CGAL_EULER_OPERATIONS_H
 
-#include <stdexcept>
-#include <algorithm>
-#include <vector>
-
 #include <boost/graph/graph_traits.hpp>
 #include <CGAL/boost/graph/properties.h>
 
@@ -27,6 +23,10 @@
 
 #include <boost/container/small_vector.hpp>
 
+#include <algorithm>
+#include <stdexcept>
+#include <vector>
+
 namespace CGAL {
 
 /// \cond SKIP_IN_MANUAL
@@ -1866,10 +1866,72 @@ bool satisfies_link_condition(typename boost::graph_traits<Graph>::edge_descript
 }
 /// \endcond
 #endif
+
+/// removes the target vertex of `h`, merging its incident edges into a single edge.
+/// \pre `degree(target(h, g), g) == 2`.
+/// \pre there is no pre-existing edge between source(h, g) and target(next(h, g), g)
+template <typename Graph>
+typename boost::graph_traits<Graph>::halfedge_descriptor
+remove_degree_2_vertex(const typename boost::graph_traits<Graph>::halfedge_descriptor h,
+                       Graph& g)
+{
+  typedef boost::graph_traits<Graph> Traits;
+  typedef typename Traits::vertex_descriptor   vertex_descriptor;
+  typedef typename Traits::halfedge_descriptor halfedge_descriptor;
+  typedef typename Traits::face_descriptor face_descriptor;
+
+  CGAL_precondition(degree(target(h, g), g) == 2);
+
+  vertex_descriptor v = target(h, g);
+  halfedge_descriptor h1 = h;
+  halfedge_descriptor h2 = opposite(next(h1, g), g);
+
+  if(is_border(h1, g))
+    std::swap(h1, h2);
+
+  vertex_descriptor v1 = source(h1, g);
+  vertex_descriptor v2 = source(h2, g);
+
+  bool exists;
+  halfedge_descriptor huv;
+  std::tie(huv, exists) = halfedge(v1, v2, g);
+  if(exists)
+    return boost::graph_traits<Graph>::null_halfedge();
+
+  if(is_border(h2, g))
+  {
+    CGAL_assertion(!is_border(h1, g));
+
+    halfedge_descriptor oh1 = opposite(h1, g);
+    halfedge_descriptor nnh1 = next(next(h1, g), g);
+    halfedge_descriptor ph2 = prev(h2, g);
+    face_descriptor f1 = face(h1, g);
+
+    set_target(h1, v2, g);
+    set_halfedge(v2, ph2, g);
+    set_next(h1, nnh1, g);
+    set_next(ph2, oh1, g);
+    set_halfedge(f1, h1, g); // in case it was nh1
+
+    remove_edge(edge(h2, g), g);
+    remove_vertex(v, g);
+
+    return h1;
+  }
+  else
+  {
+    CGAL_assertion(!is_border(h1, g) && !is_border(h2, g));
+
+    halfedge_descriptor ph1 = prev(h1, g);
+    halfedge_descriptor ph2 = prev(h2, g);
+    Euler::remove_center_vertex(h, g);
+    return Euler::split_face(ph1, ph2, g);
+  }
+}
+
 /// @}
 
 } // namespace Euler
-
 } // namespace CGAL
 
 #endif /* CGAL_EULER_OPERATIONS_H */