diff --git a/backtracking/coloring.py b/backtracking/coloring.py
index f10cdbcf9d26..abfdf16f1342 100644
--- a/backtracking/coloring.py
+++ b/backtracking/coloring.py
@@ -104,6 +104,14 @@ def color(graph: list[list[int]], max_colors: int) -> list[int]:
     >>> max_colors = 2
     >>> color(graph, max_colors)
     []
+    >>> color([], 2)  # empty graph
+    []
+    >>> color([[0]], 1)  # single node, 1 color
+    [0]
+    >>> color([[0, 1], [1, 0]], 1)  # 2 nodes, 1 color (impossible)
+    []
+    >>> color([[0, 1], [1, 0]], 2)  # 2 nodes, 2 colors (possible)
+    [0, 1]
     """
     colored_vertices = [-1] * len(graph)
 
diff --git a/machine_learning/gradient_boosting_regressor.py b/machine_learning/gradient_boosting_regressor.py
new file mode 100644
index 000000000000..7ec50346d5e4
--- /dev/null
+++ b/machine_learning/gradient_boosting_regressor.py
@@ -0,0 +1,67 @@
+"""Implementation of GradientBoostingRegressor in sklearn using the
+   boston dataset which is very popular for regression problem to
+   predict house price.
+"""
+
+import matplotlib.pyplot as plt
+import pandas as pd
+from sklearn.datasets import fetch_openml
+from sklearn.ensemble import GradientBoostingRegressor
+from sklearn.metrics import mean_squared_error, r2_score
+from sklearn.model_selection import train_test_split
+
+
+def main():
+
+    # loading the dataset from the sklearn
+    # Note: load_boston is deprecated and removed, using fetch_openml instead
+    boston = fetch_openml(name="boston", version=1, as_frame=True)
+    print(boston.keys())
+    # now let construct a data frame
+    df_boston = boston.data
+    # let add the target to the dataframe
+    df_boston["Price"] = boston.target
+    # print the first five rows using the head function
+    print(df_boston.head())
+    # Summary statistics
+    print(df_boston.describe().T)
+    # Feature selection
+
+    x = df_boston.iloc[:, :-1]
+    y = df_boston.iloc[:, -1]  # target variable
+    # split the data with 75% train and 25% test sets.
+    x_train, x_test, y_train, y_test = train_test_split(
+        x, y, random_state=0, test_size=0.25
+    )
+
+    model = GradientBoostingRegressor(
+        n_estimators=500, max_depth=5, min_samples_split=4, learning_rate=0.01
+    )
+    # training the model
+    model.fit(x_train, y_train)
+    # to see how good the model fit the data
+    training_score = model.score(x_train, y_train).round(3)
+    test_score = model.score(x_test, y_test).round(3)
+    print("Training score of GradientBoosting is :", training_score)
+    print("The test score of GradientBoosting is :", test_score)
+    # Let us evaluation the model by finding the errors
+    y_pred = model.predict(x_test)
+
+    # The mean squared error
+    print(f"Mean squared error: {mean_squared_error(y_test, y_pred):.2f}")
+    # Explained variance score: 1 is perfect prediction
+    print(f"Test Variance score: {r2_score(y_test, y_pred):.2f}")
+
+    # So let's run the model against the test data
+    fig, ax = plt.subplots()
+    ax.scatter(y_test, y_pred, edgecolors=(0, 0, 0))
+    ax.plot([y_test.min(), y_test.max()], [y_test.min(), y_test.max()], "k--", lw=4)
+    ax.set_xlabel("Actual")
+    ax.set_ylabel("Predicted")
+    ax.set_title("Truth vs Predicted")
+    # this show function will display the plotting
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()