diff --git a/include/boost/geometry/algorithms/detail/is_valid/complement_graph.hpp b/include/boost/geometry/algorithms/detail/is_valid/complement_graph.hpp
index ba54d42ba..2272bbf32 100644
--- a/include/boost/geometry/algorithms/detail/is_valid/complement_graph.hpp
+++ b/include/boost/geometry/algorithms/detail/is_valid/complement_graph.hpp
@@ -100,8 +100,8 @@ private:
     {
     public:
         has_cycles_dfs_data(std::size_t num_nodes)
-            : m_visited(num_nodes)
-            , m_parent_id(num_nodes)
+            : m_visited(num_nodes, false)
+            , m_parent_id(num_nodes, -1)
         {}
 
         inline int parent_id(vertex_handle v) const
@@ -139,7 +139,7 @@ private:
         {
             vertex_handle v = stack.top();
             stack.pop();
-            
+
             data.set_visited(v, true);
             for (typename neighbor_container::const_iterator nit
                      = m_neighbors[v->id()].begin();
@@ -205,15 +205,9 @@ public:
 
     inline bool has_cycles() const
     {
-        has_cycles_dfs_data data(m_vertices.size());
-
         // initialize all vertices as non-visited and with no parent set
-        for (vertex_handle it = m_vertices.begin();
-             it != m_vertices.end(); ++it)
-        {
-            data.set_visited(it, false);
-            data.set_parent_id(it, -1);
-        }
+        // this is done by the constructor of has_cycles_dfs_data
+        has_cycles_dfs_data data(m_num_rings + m_num_turns);
 
         // for each non-visited vertex, start a DFS from that vertex
         for (vertex_handle it = m_vertices.begin();
diff --git a/test/algorithms/is_valid.cpp b/test/algorithms/is_valid.cpp
index 3d52b4365..03b93bbe5 100644
--- a/test/algorithms/is_valid.cpp
+++ b/test/algorithms/is_valid.cpp
@@ -579,6 +579,9 @@ void test_open_polygons()
     // 1st hole touches 2nd hole at two points
     test::apply(from_wkt<OG>("POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 8,2 8,2 1),(2 5,5 8,5 5))"),
                 false);
+    // polygon with many holes, where the last two touch at two points
+    test::apply(from_wkt<OG>("POLYGON((0 0,20 0,20 20,0 20),(1 18,1 19,2 19,2 18),(3 18,3 19,4 19,4 18),(5 18,5 19,6 19,6 18),(7 18,7 19,8 19,8 18),(9 18,9 19,10 19,10 18),(11 18,11 19,12 19,12 18),(13 18,13 19,14 19,14 18),(15 18,15 19,16 19,16 18),(17 18,17 19,18 19,18 18),(1 1,1 9,9 9,9 8,2 8,2 1),(2 5,5 8,5 5))"),
+                false);
     // two holes completely inside exterior ring but touching each
     // other at a point
     test::apply(from_wkt<OG>("POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,2 9),(1 1,9 2,9 1))"),