4. Given a set of points on a plane $P=\left\{P_{1}, P_{2}, \cdots\right.$, $\left.P_{1994}\right\}$, where no three points in $P$ are collinear. Divide the points in $P$ into 83 groups arbitrarily, such that each group has at least 3 points, and each point belongs to exactly one group. Connect every pair of points within each group with a line segment, and do not connect points from different groups. This results in a graph $G$. Clearly, different ways of connecting the line segments result in different graphs. The number of triangles in $G$ with vertices from $P$ is denoted as $m(G)$.
(1) Find the minimum value $m_{0}$ of $m(G)$;
(2) Let $G^{*}$ be a graph such that $m\left(G^{*}\right)=m_{0}$. If the line segments in $G^{*}$ are colored using 4 different colors, with each line segment colored exactly one color, then there exists a coloring method such that after coloring, $G^{*}$ contains no monochromatic triangles.
4. (1) Let the number of points in each group be $x_{1}, x_{2}, \cdots, x_{83}$, then $x_{1}+x_{2}+\cdots+x_{83}=1994$, and $m(G)=\mathrm{C}_{x_{1}}^{3}+$ $\mathrm{C}_{x_{2}}^{3}+\cdots+\mathrm{C}_{x_{6}}^{3}$, (*)

If $x_{1}-x_{2}>1$, then move one point from the first group to the second group. Because
$\mathrm{C}_{x_{1}-1}^{3}+\mathrm{C}_{x_{1}+1}^{3}-\mathrm{C}_{x_{1}}^{3}-\mathrm{C}_{x_{2}}^{3}=\mathrm{C}_{x_{1}-1}^{3}+\mathrm{C}_{x_{2}}^{3}-$ $\mathrm{C}_{x_{1}-1}^{3}-\mathrm{C}_{x_{1}-1}^{2}-\mathrm{C}_{x_{2}}^{3}=\mathrm{C}_{x_{3}}^{2}-\mathrm{C}_{x_{1}-1}^{2}<0, m(G)$ will decrease. Therefore, when $m(G)$ is minimized, the difference between any two $x_{i}$ is $\leqslant 1$.
Since $1994=83 \times 24+2=24 \times 81+2 \times 25$,
the only way to group the points to minimize $m(G)$ is: 81 groups each containing 24 points, 2 groups each containing 25 points. At this time, $m_{0}$ $=81 \mathrm{C}_{24}^{3}+2 \mathrm{C}_{25}^{3}=168544$.
(2) Color the 25-point groups as follows: divide the points into 5 groups: $y_{1}, y_{2}, y_{3}, y_{4}, y_{5}$, each group containing 5 points; color the segments within each group according to Figure (A) with two colors $a, b$; color the connections between different groups according to Figure (B) with two other colors $c, d$.

With this coloring, there are no monochromatic triangles. For the 24-point groups, simply remove one point and all the segments connected to it from a 25-point group, ensuring no monochromatic triangles appear.