4. Given a set of points on a plane $P=\left\{P_{1}, P_{2}, \cdots, P_{1994}\right\}$, where no three points in $P$ are collinear. Divide all points in $P$ into 83 groups arbitrarily, such that each group has at least 3 points, and each point belongs to exactly one group. Then connect any two points in the same group with a line segment, and do not connect points in different groups, thus obtaining a pattern $G$. Different grouping methods result in different patterns, and the number of triangles in pattern $G$ with vertices from $P$ is denoted as $m(G)$.
(1) Find the minimum value $m_{0}$ of $m(G)$;
(2) Let $G^{*}$ be a pattern such that $m\left(G^{*}\right)=m_{0}$. If the line segments in $G^{*}$ (referring to line segments with endpoints from $P$) are colored with 4 colors, and each line segment is colored with exactly one color, prove that there exists a coloring scheme such that $G^{*}$, after coloring, contains no triangle with vertices from $P$ and all three sides of the same color.
(1) Take any pattern $G^{*}, G^{*}$ obtained from groups $X_{1}, X_{2}, \cdots, X_{83}$, where $X_{i}$ is the set of points in the $i$-th group, $i=1,2, \cdots, 83$. Let $\left|X_{i}\right|=x_{i}(i=1,2, \cdots, 83)$, then $x_{1}+x_{2}+\cdots+x_{83}=1994$, and $m_{0}=C_{x_{1}}^{3}+C_{x_{2}}^{3}+\cdots+C_{x_{83}}^{3}$.
The following proves that when $1 \leqslant i \neq j \leqslant 83$, $\left|x_{i}-x_{j}\right| \leqslant 1$.
Otherwise, if there exist $i, j(1 \leqslant i \neq j \leqslant 83)$, such that $\left|x_{i}-x_{j}\right| \geqslant 2$, without loss of generality, assume $x_{i}>x_{j}$, construct the partition of $P$'s points $Y_{1}, Y_{2}, \cdots, Y_{83}\left(Y_{i}\right.$ is the set of points in the $i$-th group, $\left.i=1,2, \cdots, 83\right)$,
such that $y_{k}=\left|Y_{k}\right|=\left\{\begin{array}{l}x_{k}, k \neq i, j \\ x_{i}-1, k=i, \\ x_{j}+1, k=j .\end{array}\right.$ For the pattern $G^{\prime}$ obtained from the partition $Y_{1}, Y_{2}, \cdots, Y_{83}$, $m\left(G^{\prime}\right)=C_{y_{1}}^{3}+C_{y_{2}}^{3}+\cdots+C_{y_{83}}^{3}$. Therefore, $m\left(G^{\prime}\right)-m_{0}=C_{y_{i}}^{3}+C_{y_{j}}^{3}-C_{x_{i}}^{3}-C_{x_{j}}^{3}$ $=C_{x_{i}-1}^{3}+C_{x_{j}+1}^{3}-C_{x_{i}}^{3}-C_{x_{j}}^{3}=C_{x_{j}}^{2}-C_{x_{i}-1}^{2}$,
and $x_{i}-x_{j} \geqslant 2 \Rightarrow x_{i}-1 \geqslant x_{j}+1>x_{j} \Rightarrow C_{x_{i}-1}^{2}<C_{x_{j}}^{2} \Rightarrow m\left(G^{\prime}\right)-m_{0}<0$, which contradicts the minimality of $m_{0}$. Thus, noting that $1994=83 \times 24+2=81 \times 24+2 \times 25$, we have $m_{0}=81 C_{24}^{3}+2 C_{25}^{3}=168544$.
(2) Suppose the pattern $G^{*}$ is obtained from the partition $X_{1}, X_{2}, \cdots, X_{83}$. By (1), without loss of generality, assume $\left|X_{1}\right|=\left|X_{2}\right|=\cdots=\left|X_{81}\right|=24,\left|X_{82}\right|=\left|X_{83}\right|=25$.
The graph formed by the set $X_{i}$ and the connected line segments is called the $i$-th block of $G^{*}$, denoted as $G_{i}^{*}, i=1,2, \cdots, 83$. For $G_{83}^{*}$, let $X_{83}=Y_{1} \bigcup Y_{2} \bigcup Y_{3} \bigcup Y_{4} \cup Y_{5}$, such that $Y_{i} \cap Y_{j}=\varnothing(1 \leqslant i \neq j \leqslant 5)$, $\left|Y_{i}\right|=5(1 \leqslant i \leqslant 5)$. Color the line segments connecting any two points in each subset $Y_{i}(1 \leqslant i \leqslant 5)$ using the method shown in the left figure below, and color the line segments connecting different subsets $Y_{i}$ and $Y_{j}(i \neq j)$ using the method shown in the right figure below, where $a, b, c, d$ represent four different colors. The colored $G_{83}^{*}$ clearly does not contain a triangle with the same color.
For $G_{82}^{*}$, refer to the method for $G_{83}^{*}$ for coloring. For $G_{i}^{*}(1 \leqslant i \leqslant 81)$, first add a point and connect it to the original 24 points with a line segment each, then color according to the method for $G_{83}^{*}$, and finally remove the added point and the line segments connected to it. The resulting $G_{i}^{*}$ clearly does not contain a triangle with the same color.
In summary, there exists a coloring scheme such that the colored $G^{*}$ does not contain a triangle with the same color on all three sides, with the points of $P$ as vertices.