4. Given 9 points in space, where no 4 points are coplanar. Find the smallest natural number $n$, such that when any $n$ line segments are drawn between the given 9 points and each line segment is colored either red or blue, there will always exist a monochromatic triangle.

In space, given 9 points, where no 4 points are coplanar. Find the smallest natural number $n$, such that when any $n$ line segments are drawn between the given 9 points and each line segment is colored either red or blue, there will always exist a monochromatic triangle.
Solution: First, if every two points are connected by a line segment, i.e., $\mathrm{C}_{9}^{2}=$ 36 edges are connected, then $K_{9}$ exists.

If 36-1 edges are connected, then $K_{8}$ exists; if 36-2 edges are connected, then $K_{7}$ exists;

If 36-3 edges are connected, then $K_{6}$ exists, and by Theorem 1, monochromatic triangles exist in all cases.
Therefore, $n_{\min } \leqslant 33$.
If $n=32$. Divide the 9 points into 5 groups, with 4 groups each containing 2 points, and the remaining group containing 1 point. Arrange these 5 groups clockwise on a circle, connect red edges between adjacent groups, and blue edges between non-adjacent groups, with no edges within the same group. In this way, $n=32$. If there is a monochromatic triangle, the three points of this triangle must belong to different groups, but such 3 groups must include 2 adjacent groups and 2 non-adjacent groups, so this triangle cannot be monochromatic, leading to a contradiction! Therefore, $n_{\min }=33$.