diff --git a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/sdg_br_case1.cpp b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/sdg_br_case1.cpp
index 564ce2d5070..60962b91009 100644
--- a/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/sdg_br_case1.cpp
+++ b/Segment_Delaunay_graph_2/test/Segment_Delaunay_graph_2/sdg_br_case1.cpp
@@ -13,7 +13,26 @@ typedef K::Segment_2 Segment_2;
 typedef CGAL::Segment_Delaunay_graph_traits_2<K> Gt;
 typedef CGAL::Segment_Delaunay_graph_2<Gt> SDG;
 
-int main(int argc,char**)
+void case1()
+{
+  SDG                    sdg;
+
+  SDG::Vertex_handle v0=sdg.insert(Point_2(144, 736));
+  SDG::Vertex_handle v1=sdg.insert(Point_2(368, 736));
+  SDG::Vertex_handle v2=sdg.insert(Point_2(144 , 672));
+  SDG::Vertex_handle v3=sdg.insert(Point_2(368 , 672));
+
+  sdg.insert(v0,v1);
+  sdg.insert(v2,v3);
+
+  sdg.insert(Point_2(192, 704));
+  sdg.insert(Point_2(320, 704));
+  sdg.insert(Point_2(256, 704));
+
+  assert(sdg.is_valid());
+}
+
+void case2()
 {
   SDG                    sdg;
 
@@ -35,3 +54,52 @@ int main(int argc,char**)
 
   assert(sdg.is_valid());
 }
+
+void case3()
+{
+  SDG                    sdg;
+
+  SDG::Vertex_handle v0=sdg.insert(Point_2(96, 544));
+  SDG::Vertex_handle v1=sdg.insert(Point_2(416,544 ));
+  SDG::Vertex_handle v2=sdg.insert(Point_2(416, 384));
+  SDG::Vertex_handle v3=sdg.insert(Point_2(96, 384));
+
+  sdg.insert(v0,v1);
+  sdg.insert(v1,v2);
+  sdg.insert(v2,v3);
+  sdg.insert(v3,v0);
+
+  sdg.insert(Point_2(256, 464));
+  sdg.insert(Point_2(272, 416));
+
+  assert(sdg.is_valid());
+}
+
+void case4()
+{
+  SDG                    sdg;
+
+  SDG::Vertex_handle v2=sdg.insert(Point_2(416, 384));
+  SDG::Vertex_handle v3=sdg.insert(Point_2(96, 384));
+  sdg.insert(v2,v3);
+
+  sdg.insert(Point_2(416, 464));
+  sdg.insert(Point_2(96, 464));
+
+  sdg.insert(Point_2(176, 544));
+  sdg.insert(Point_2(336, 544));
+  sdg.insert(Point_2(256, 464));
+  sdg.insert(Point_2(272, 416));
+
+  assert(sdg.is_valid());
+}
+
+// missing test case: is_interior_in_conflict_touch, s!=r, vpqr!=ZERO and p or q a point
+
+int main()
+{
+  case1();
+  case2();
+  case3();
+  case4();
+}