The python package `networkx` contains an implementation of the Christofides algorithm. You can install `networkx` with the following command:
```console
pip install networkx
```

Here is how you could rewrite the above code using the Christofides algorithm:

```py
from networkx import Graph
from networkx.algorithms.approximation.traveling_salesman import christofides

def tsp(points):
    # calculate the distance between all points
    def distance(p1, p2):
        x1, y1 = p1
        x2, y2 = p2
        return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

    # create the distance graph
    distance_graph = Graph()
    for i in range(len(points)):
        for j in range(len(points)):
            distance_graph.add_edge(i, j, weight=distance(points[i], points[j]))

    # find TSP path
    path = christofides(distance_graph)

    # calculate length of path
    length = 0
    for i in range(len(points)):
        length += distance_graph.get_edge_data(path[i], path[i+1])["weight"]
    return length, path

points = [(0, 0), (1, 2), (3, 4), (5, 6)]
length, path = tsp(points)
print("Shortest path is: " + str(path))
print("Distance: " + str(length))
```

Be careful as this algorithm is not guaranteed to give the optimal solution. The Christofides algorithm sacrifices accuracy for speed, running in $O(n^3)$ time (rather than $O(n!)$), but only guaranteeing a 3/2 approximation.
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