diff --git a/sklearn/tree/export.py b/sklearn/tree/export.py
index ff1355db478ee..5f58aed546bfc 100644
--- a/sklearn/tree/export.py
+++ b/sklearn/tree/export.py
@@ -152,8 +152,11 @@ def get_color(value):
             # Classification tree
             color = list(colors['rgb'][np.argmax(value)])
             sorted_values = sorted(value, reverse=True)
-            alpha = int(np.round(255 * (sorted_values[0] - sorted_values[1]) /
-                                 (1 - sorted_values[1]), 0))
+            if len(sorted_values) == 1:
+                alpha = 0
+            else:
+                alpha = int(np.round(255 * (sorted_values[0] - sorted_values[1]) /
+                                           (1 - sorted_values[1]), 0))
         else:
             # Regression tree or multi-output
             color = list(colors['rgb'][0])
@@ -310,7 +313,7 @@ def recurse(tree, node_id, criterion, parent=None, depth=0):
                         # Find max and min impurities for multi-output
                         colors['bounds'] = (np.min(-tree.impurity),
                                             np.max(-tree.impurity))
-                    elif tree.n_classes[0] == 1:
+                    elif tree.n_classes[0] == 1 and len(np.unique(tree.value)) != 1:
                         # Find max and min values in leaf nodes for regression
                         colors['bounds'] = (np.min(tree.value),
                                             np.max(tree.value))
diff --git a/sklearn/tree/tests/test_export.py b/sklearn/tree/tests/test_export.py
index 8a7421923b152..8d954d3cc2526 100644
--- a/sklearn/tree/tests/test_export.py
+++ b/sklearn/tree/tests/test_export.py
@@ -18,6 +18,7 @@
 y = [-1, -1, -1, 1, 1, 1]
 y2 = [[-1, 1], [-1, 1], [-1, 1], [1, 2], [1, 2], [1, 3]]
 w = [1, 1, 1, .5, .5, .5]
+y_degraded = [1, 1, 1, 1, 1, 1]
 
 
 def test_graphviz_toy():
@@ -207,6 +208,20 @@ def test_graphviz_toy():
 
     assert_equal(contents1, contents2)
 
+    # Test classifier with degraded learning set
+    clf = DecisionTreeClassifier(max_depth=3)
+    clf.fit(X, y_degraded)
+
+    out = StringIO()
+    export_graphviz(clf, out_file=out, filled=True)
+    contents1 = out.getvalue()
+    contents2 = 'digraph Tree {\n' \
+                'node [shape=box, style="filled", color="black"] ;\n' \
+                '0 [label="gini = 0.0\\nsamples = 6\\nvalue = 6.0", fillcolor="#e5813900"] ;\n' \
+                '}'
+
+    assert_equal(contents1, contents2)
+
 
 def test_graphviz_errors():
     # Check for errors of export_graphviz